MATH 1

Activity 2: Let “” represent “x”, and “♪” represent “1”. Write what each set ofpicture/s represents using “x” as the variable and a number (constant). Item nos. 1and 2 are done for you. Picture Algebraic Expression x1.  x+32.  ♪♪♪3.  ♪♪♪♪♪♪4. ♪♪ 5.  ♪♪♪Your answers must be like these. Algebraic Expression 3. 3x + 6 4. 2 + 5x 5. 2x + 3 Did you know? Verbal phrases involving quantities can be translated into algebraic expressions.Constants and variables together with symbols of operations and relations are important intranslating verbal phrases into algebraic expressions. 10

Remember this . . . The symbols of operations and relations used in algebra are as follows:Symbol Meaning + addition, plus, increased by, added to, the sum of, more than - subtraction, minus, decreased by, subtracted from, less than, diminished by ·,( ) multiplication, times, multiplied by /,÷ division, divided by, ratio of, the quotient of = Equals, is equal to < is less than > is greater than ≤ is less than or equal to ≥ is greater than or equal to ≠ is not equal to Historical Note ALGEBRA HAD ITS BEGINNINGS in ancient Egypt and Babylon,where people learned to solve linear (ax = b) and quadratic (ax2 + bx = c)equations, as well as indeterminate equations such as x2 + y2 = z2, wherebyseveral unknowns are involved. The ancient Babylonians solved arbitraryquadratic equations by essentially the same procedures taught today. 11

Activity 3: Study how each of the following verbal phrases are translated intoalgebraic expressions.Study ThisTranslate each verbal phrase into an algebraic expression. Verbal Phrase Algebraic Expression1. Sum of two numbers a+b2. Twice a certain number 2n3. Difference of 8 and thrice a certain number 8 – 3b4. Quotient of a number and 3 diminished by 2 x –2 35. Square of the sum of a number and 2 (x + 2)2 Any letter or variable can represent the numbers because the numbers arenot known. In item #1, a and b are the symbols used to represent the said numbers.We add them because of the word ‘sum’, hence the use of the plus sign (+). Item #2, the variable n represents the number. The phrase is translated asthe product of 2 and n. Item #3, the variable b represents the number and is used as a coefficient of3. Their product is subtracted from 8 because of the word ‘difference’. Item #4, the variable x represents the number with 3 as its denominatorbecause of the word ‘quotient’. The phrase ‘diminished by 2’ is translated as – 2. Item #5, the variable represents the number added to 2. Because of the wordsquare, the quantity (x + 2) is raised to the second power.12

Try ThisA. Translate each verbal phrase into an algebraic expression.Verbal Phrase Algebraic Expression1. A number y increased by four2. Three times a number m decreased by 63. Nine added to the quotient of m and fiveB. Translate each algebraic expression into a verbal phrase.Algebraic Expression Verbal Phrase4. 8n – 125. 2(x + y)6. x2 + 3 Check your answers. If you have understood the examples, you should haveanswered all of the items correctly. Your answers in letter A should be the same asthe expressions found in the Table A and your answers in letter B should bestatements having the same meaning as the statements found in the Table B. Table A 1. y + 4 2. 3m – 6 3. 9 + (m/5) 13

Table B 4. a) The difference between eight times the number n and twelve b) The product of eight and the number n minus twelve c) Eight times the number n decreased by twelve d) Twelve less than eight times the number n. 5. a) Twice the sum of the numbers x and y b) Two times the sum of the numbers x and y c) Two multiplied by the sum of the numbers x and y d) The product of two and the sum of two numbers x and y 6. a) The sum of the square of the number x and three b) The square of the number x increased by three c) Three more than the square of the number x d) Three added to the square of the number x Self-check 2 Do you remember me? I pioneered the use of symbolsin representing numbers and I’m quite well known for that. Answer the matching testto know me. Matching Test: Directions: Match each verbal phrase in Column A with thealgebraic expressions in column B. Write the letter of your answer on the blank provided 14

before the item number. Read the word formed by the answers to identify the personabove.Answer Column A Column B 1. The square of six minus the number x a) ab + 20 2. Two more than six times the number n d) 62 – x 3. Three times a number x decreased by five h) 5(3m) 4. The quotient of sixteen and the number n i) 6n + 2 5. Five times the product of the number m and three n) 9 + (m÷n) 6. Twenty added to the product of the numbers a and b o) 3x – 5 7. Nine increased by the quotient of the numbers m and n p) 16 ÷ n 8. The product of twelve and the number y divided by seven s) 4m+(n÷3) 9. Eight subtracted from the sum of eleven and the number y t) 12y/7 10. The sum of product of four and the number m and the u) (y+11) - 8 quotient of the number n and three Answer Key on page 25Lesson 3: Simplifying Numerical Expressions Involving Grouping Symbols and Exponents “Can You Simplify Me? If Yes, HOW?” Algebra uses the set of grouping symbols = {( ), { }, [ ]}. Parentheses ( ), braces { },brackets [ ], and the vinculum ¯ are used to show that the numerals they enclose aretreated as one quantity. 22 + 32 means the square of 2 added to the square of 3 but (2 + 3)2read as two plus three quantity squared, means the sum of 2 and 3 is the single quantitythat must be squared. – (a + b) means that the subtrahend is the sum of a and b. With the knowledge of these different symbols, we can simplify numericalexpressions into a single quantity. 15

Activity 1: Learn from the following examples how each numerical expression with grouping symbols and exponent/s is simplified.Study ThisIllustrative Example 1: Simplify the expression 10 – [(15 – 10) + 32].= 10 – [(15 – 10) + 32]= 10 – [5 + 9] Computing 15 – 10 and squaring 3= 10 – [14] Adding 5 and 9= 10 –14 Removing the [ ] preceded by ‘-‘ sign=-4 Subtracting 14 from 10Illustrative Example 2: Simplify the expression – 2 + {23 – [32 – (12 + 5) + 4] + 52}.= – 2 + {23 – [32 – (12 + 5) + 4] - 24}= - 2 + {8 – [9 – (17) + 4] – 16} Squaring the terms and computing 12 + 5= - 2 + {8 – [9 – 17 + 4] - 16} Removing the ( ) preceded by -= - 2 + {8 – [ - 4] – 16} Computing 9 – 17 + 4= - 2 + {8 + 4 – 16} Removing the [ ] preceded by -= - 2 + {- 4} Computing 8 + 4 - 16=-2–4 Removing the { } preceded by ‘+’ sign=-6 Subtracting 4 from – 2Illustrative Example 3: Simplify the expression 2(5–3)2 – {7– [4–(23 – 5)+1] – 2(3)}.= 2(5–3)2 – {7– [4–(23 – 5)+1] – 2(3)}= 2(2)2 – {7 – [4 - (8 – 5) + 1] – 6} Computing 5–3, -2(3), getting the cube of 2= 2(4) – {7 – [4 – (3) + 1] – 6} Squaring 2 and computing 8 - 5= 8 – {7 – [4 – 3 + 1] – 6} Computing 2(4) and removing ( ) preceded by ‘-‘ sign= 8 – {7 – [2] – 6} Computing 4 – 3 + 1= 8 – {7 – 2 – 6} Removing the [ ] preceded by ‘-‘ sign= 8 – {- 1} Computing 7 – 2 - 6=8+1 Removing the { } preceded by ‘-‘ sign= 9 Adding 8 and 1 16

Did you know? Some expressions contain more than one grouping symbol. Parentheses ( ),brackets [ ], and braces { } are all grouping symbols used in algebra. When an expressioncontains more than one grouping symbol, the computations in the innermost groupingsymbols should be done first. When a term is raised to an exponent higher than 1 like inthe illustrative example #2: – 2 + {23 – [32 – (12 + 5) + 4] - 24}, find the power first beforeperforming the operation/s. When a mathematical phrase within a pair of grouping symbolsis raised to an exponent higher than 1 like in illustrative example #3: 2(5–3)2 – {7– [4–(23 –5)+1] – 2(3)}, perform the indicated operation within the grouping symbol first beforegetting the power of the quantity which results in 2(2)2 – {7 – [4 - (8 – 5) + 1] – 6} = 2(4) –{7 – [4 – (3) + 1] – 6}. Remember These. . .Steps in simplifying numerical expressions involving grouping symbols and exponents  Get the power of the terms with exponents higher than one.  Remove grouping symbols like ( ), [ ], and { } by simplifying the enclosed phrase, beginning from the innermost pair.  Perform all multiplication and division operations from left to right whichever comes first.  Perform all addition and subtraction operations from left to right.Critical Thinking: Use each of the numbers 2, 4, 6, 8, and 10 exactly once, with any operation sign and grouping symbol, to write an expression equal to 10.Error Analysis: When Bob simplified the expression 72 ÷ 6 + 3, his answer was 8. What was Bob’s error? 17

Try This AnswerSimplify the following numerical expressions. Numerical Expression 1. 32 + 6 – (52 – 20) 2. 10 - (20 ÷ 4) - 32 3. [(6 + 23) – 7] + [4 - (24 ÷ 23)] 4. 2 [(15 –23) + 32 - (20 ÷ 5) – 10] If you answered the items above following the steps mentioned, you should haveobtained the following answers. 1) 10; 2) – 4; 3) 8; & 4) 4.Self-check 3 Why are variables used to represent numbers? It is because of ____________. To find the answer to this question, simplify each numerical expression below bygetting the powers and removing the grouping symbols. Then match each item in column Ato the options in column B. Write only the letter of your answer. Column A Column B (Numerical Expressions) (Options)1. – 1 – [3 + (23 – 32) - 2]2. 2 + [(32 ÷ 3) – (52 – 20)] g) 23. – 2 +[ - 4 + (52 – 32) ÷ 2] a) - 14. [(20 -25) + (10 + 2)] – [(36 ÷ 4) – 5] m) 55. 2 [3 + (22 – 7)] + 42 – (8 + 4) b) 46. [(52 – 32) ÷ 2] l) 07. {[10 – (20 ÷ 4) ] ÷ 5} - 2 e) 3 r) 8 Answer Key on page 25 18

Lesson 4: Evaluating Algebraic Expressions Can you think of an instance when substitution is done? In abasketball game, a better player usually replaces a player who does not perform well, ormaybe one player needs some rest so another player has to come in. Replacing oneplayer by another player is called substitution. In Algebra, we replace a variable with anumber. This is called substituting the variable. To evaluate an algebraic expression,substitute the variable by a number and simplify the expression. Evaluating an algebraicexpression means obtaining or computing the value of the expression where value/sof the variable/s is/are assigned. Study ThisIllustrative example 1: Evaluate 2y + 3 when y = 3 Substituting y by 3 Solution: = 2(3) + 3 Multiplying 2 and 3 =6+3 Adding 6 and 3 =9Illustrative example 2: Evaluate 3(a + 4) + (a – 2) when a = 6Solution: = 3(6 + 4) + (6 – 2) Substituting a by 6= 3(10) + 4 Computing 6 + 4 and 6 - 2= 30 + 4 Multiplying 3 and 10= 34 Adding 30 and 4Illustrative example 3. Evaluate 2(x + 4) + 3(y – 3) when x = - 3 and y = 5Solution: = 2(-3 + 4)+3(5–3) Substituting x by 4 and y by 5= 2(1) + 3(2) Computing -3 + 4 and 5 - 3=2+6 Computing 2(1) and 3(2)= 8 Computing 2 + 6 19

Illustrative Example 4. Evaluate (2x ÷ 3) - 2y + 2y2 when x = - 6, y = 3Solution: = [2(-6)÷3]-2(3)+2(3)2 Substituting x by –6 and y by 3 = [-12 ÷ 3] - 6 + 2(9) Computing 2(-6); -2(3) and (3)2 = - 4 - 6 + 18 Computing -12 ÷ 3 and 2(9) = 8 Computing – 4 – 6 +18 So, are you now familiar with how the substitution is done? We replace the variablewith its given value. Then we simplify the expression the way we did in the previous lessonby applying the rules on simplifying expressions. Try ThisEvaluate each of the following expressions. Use the given value of each variable.Algebraic Expression Assigned value/s of the variable/s1. 7a + 3b a = -4 b=22. 4xy - 2(x + y) – y2 x = 3 y=43. (3y + y) + y2 y = -54. 3(m – n) + (6m ÷ n) m = 6 n = -45. (4x2 ÷ y) + 3(x - y) x = -3 y=6Once you are done, you may check your answers against mine.1. 7a + 3b if a = -4 and b =2 2. 4xy - 2(x + y) – y2 if x = 3 and y = 4 = 7(-4) + 3(2) = 4(3)(4) – 2(3+4) – (4)2 = -28 + 6 = 48 – 14 - 16 = -22 = 183. (3y + y) + y2 if y = - 5 4. 3(m – n) + (6m ÷ n) if m = 6and n = -4 = [3(-5) + (-5)] + (-5)2 = 3[6 – (-4)] + [6(6) ÷ (-4)] = [-15 – 5] +25 = 3[6 + 4] + [36 ÷ (-4)] = [-20] + 25 = 3[10] + [-9] = -20 + 25 = 30 – 9 =5 = 21 20

5. (4x2 ÷ y) + 3(x - y) if x = -3 and y = 6 = [4(-3)2 ÷ 6] + 3[(-3) – 6] = [4(9) ÷ 6] + 3[-3 – 6] = [36 ÷ 6] + 3[-9] = 6 –18 = - 12Self-check 4Choose the value/s of the variable/s that satisfy the given equation. Write theletter of your answer on the blank provided before the item number.Example: _b_ (n + 6 = 10)a) n = 10 b) n = 4 c) n = -4_____ 1. 2ab = 6 b) a = 1, b = 3 c) a = 1, b = 2 a) a = 2, b = 3_____ 2. x + 6 = -5 b) x = -10 c) x = -11 a) x = 11_____ 3. y – 7 = -12 b) y = 5 c) y = 19 a) y = -5_____ 4. (y/2) = 9 b) y = 9 c) y = 18 a) y = -18_____ 5. 3x - (x + 8) = - 2 b) x = 2 c) x = -3 a) x = 3 Answer Key on page 25 21

Let’s summarizeA. Key Terms Algebraic expression is a symbol or set of symbols resulting from the application of one or more fundamental operations of addition, subtraction, multiplication, and division to constants and variables. Constant is a symbol that has a fixed value. Numerical expression is a mathematical phrase, which does not contain a variable. It is also called a number phrase. Open phrase is a mathematical phrase that contains variable/s. Term is expressed as a product or quotient of coefficients. Terms are parts of an algebraic expression separated by plus or minus signs. Variable is a symbol having no fixed value; a symbol that could take more than one value.B. Key Points 1. To simplify a numerical expression involving exponents and grouping symbols, a) get the powers of the terms with exponents higher than one, b) perform the indicated operation/s within a grouping symbol following the MDAS rule, c) remove grouping symbols starting from the innermost. 2. The process of finding the value of an algebraic expression is called evaluating an algebraic expression. 3. A term without an indicated numerical coefficient is understood to have 1 as the numerical coefficient. 4. A term without an indicated literal coefficient is called a constant term. 22

What to do after (Posttest)Direction: Choose the letter of the correct answer.1. It is an expression that is made up of one or more terms joined by + or - signs.a. numerical expression c. mathematical sentenceb. algebraic expression d. verbal expression2. It is a part of an algebraic expression that has a fixed value.a. variable b. term c. phrase d. constant3. What is the constant term in the expression 2x – 3?a. -3 b. 2 c. 3 d. 2 and – 34. What is the simplest form of the numerical expression 5 + (16 ÷ 4) – 23?a. – 7 b. – 1 c. 1 d. 75. Which is the mathematical translation of the phrase “two times a number n decreasedby ten”?a. 2(n – 10) b. 10 – 2n c. 2n – 10 d. 2(10 - n)6. What is the constant in the expression – a2b? d. – 1 a. 2 b. 1 c. 07. Which of the following is NOT the verbal phrase of the expression 6 + 2b?a. Twice a number b more than 6 c. The sum of 6 and twice the number bb. Six increased by twice the number b d. Twice the sum of 6 and the number b8. What is the value of the expression 2x + y – 6 when x = -2 and y = 3?a. 7 b. 1 c. – 2 d. – 79. Of the following, which is a numerical expression?a. 2x + 4 b. 3 – 6 + y c. 2ab d. 2(9 – 14)10. Evaluate 3(a + 2b), if a = 5 and b = -5a. -15 b. 15 c. 25 d. 4511. How is the numerical expression (3 – 5)2 simplified? a. Subtract the square of 5 from 3. b. Multiply the difference of 3 and 5 by 2 c. Square both 3 and 5 then find their difference. d. Find the difference of 3 and 5 then square the result. 23

12. In simplifying an algebraic expression containing the grouping symbols written in theform [ ( { } ) ], , which grouping symbol is to be removed first?a. [ ] b. ( ) c. { } d. any13. What is the value of x if 2x – 3 is equal to 5?a. – 4 b. – 1 c. 1 d. 414. If x = 1 and y = - 1, what is the value of the expression 3x2 – 3y2? a. 0 b. 6 c. 8 d. 1215. Which of the following is the mathematical translation of the phrase ‘three more thanfour-fifths of a number x’?a. 4x + 3 b. 3 > 4x c. 4 (x+3) d. 4x > 3 5 5 5 5 Answer Key on page 25 24

Answer Key Pre-Test page 3 1. d 6. b 11. d 2. c 7. b 12. b 3. b 8. c 13. c 4. d 9. b 14. c 5. b 10. b 15. a Lesson 1 Self-Check 1 A page 7 Terms Constant/s Variable/s 1. a and 6 1 and 6 a 2. – 4b -4 b 3. 5x and – 2 5 and – 2 x 4. 3m 3m 5. n/8 1/8 n Lesson 1 Self-Check 1 B page 7 1. A 6. A 2. A 7. N 3. A 8. A 4. N 9. N 5. N 10. NLesson 2 Self-Check 2 page 14 Lesson 3 Self-Check page 181. d 6. a 1. a 6. r2. i 7. n 2. l 7. a3. o 8. t 3. g4. p 9. u 4. e5. h 10. s 5. b Lesson 4 Self-Check page 211 234 5b cac a1. b Post Test page 23 11. d2. d 6. d 12. c3. a 7. d 13. d4. c 8. d 14. a5. c 9. d 15. a 10. a END OF MODULE 25

BIBLIOGRAPHYCariño, I. D. (1999). Elementary algebra for high school: Integrating desirable Filipino values II . Pasig City: Anvil Publishing Inc.Charles, R. I. and Thompson, A. G. (1996). Secondary math: An integrated approach focus on algebra. USA: Addison-Wesley Publishing Company.Dugopolski, M. (2001). Algebra for college students. (2nd ed.) Singapore: McGraw-Hill Book Co.Malaborbor, P. B. et al. (2002). Elementary algebra for the basic education curriculum. Metro Manila: Diamond Offset Press. 26

Module 7 Terms and Powers What this module is all about This module is basically a continuation of the lessons in Module 6. Specifically, itdeals with the terms of an algebraic expression, coefficient/s, base, and exponents in aterm, simplification of monomials with the application of the laws of exponents, operationson monomials and scientific notation. The lessons in this module will help you identify the parts of a term such as thenumerical and literal coefficients, and the exponents of the bases in a term. It will alsoenable you to classify similar or dissimilar terms. Likewise, the module will discuss how thelaws of exponents work in the simplification of monomials, and how to write numbers inscientific notation. This consists of the following lessons: Lesson 1 Terms Lesson 2 The Base and Exponent in a Term Lesson 3 Simplifying Terms Using the Laws of Exponents Lesson 4 Operations on Terms Lesson 5 Scientific Notation What you are expected to learn After going through this module, you are expected to: • determine if terms are similar or dissimilar; • identify the base, coefficient and exponent in a term; • simplify a term using the laws on exponents; • perform operations on terms; and • express numbers in scientific notation. 1

How to learn from this moduleThis is your guide for the proper use of the module: 1. Read the items in the module carefully. 2. Follow the directions as you read the materials. 3. Answer all the questions that you encounter. As you go through the module, you will find help to answer these questions. Sometimes, the answers are found at the end of the module for immediate feedback. 4. To be successful in undertaking this module, you must be patient and industrious in doing the suggested tasks. 5. Take your time to study and learn. Happy learning! The following flowchart serves as your quick guide in using this module. Start Take the Pretest Check your paper and count your correct answers. Is your score Yes Scan the items you 80% or above? missed. No Proceed to the nextStudy this module module/STOP.Take the Posttest 2

What to do before (Pretest) Slow Down!Answer the pretest first before you proceed with the module.PretestDirections: Read each item carefully and choose the letter of the correct answer.1. If two terms have the same literal coefficients, then they are called __________.a. Like terms b. Dissimilar terms c. Similar Terms d. Both a and c2. What is m in the term 12m? c. It is the numerical coefficient of 12. a. It is the exponent of 12. d. It is the literal coefficient of the term. b. It is the literal coefficient of 12.3. How many terms are there in the expression 3x – 2y + 5?a. 1 b. 2 c. 3 d. 44. In the expression − ab , which of the following statements is NOT correct? 3a. −1 is the numerical coefficient of ab. c. a is a coefficient of − b . 33b. - ab is the coefficient of 3. d. –b is a coefficient of a . 35. What is the sum of 6x, - 4x, and – 7x?a. -5x b. 5x c. 9x d. -9x6. What is/are the base/s in the term 5x2? d. 5 and x a. 5 b. x c. x27. What is the product of 4x2 and -2x3?a. -8x6 b. -8x5 c. 8x5 d. 8x68. What is the quotient of 12x4y5 and -3x3y3?a. 4x7y8 b. - 4x7y8 c. -4xy2 d. 4xy2 3

9. When a number is written in scientific notation, where is the decimal point located? a. Decimal point is located between the last two digits of the given number. b. Decimal point is located after the last non-zero digit of the given number. c. Decimal point is located after the first non-zero digit of the given number. d. Decimal point is located between any two non-zero digits of the number.10. What is the difference when 5m2 is subtracted from -7m2? a. -12m2 b. -12m4 c. 12m2 d. -1211. What is 25 643 in scientific notation? a. 2.5643 x 104 b. 2.5643 x 10-4 c. 25.643 x 103 d. 25.643 x 10-312. What is the product of 23x5 and 2x3? a. 44x8 b. 23x8 c. 24x8 d. 12x813. What is the simplest form of the expression x4 y2 ? x2 y3 a. xy b. x2 c. x2y d. x6 y y514. What is 2.5 x 104 in standard notation? a. 25.00 b. 250.00 c. 2500.0 d. 2500015. Which of the following sets contains similar terms? ( )a. − 2x6 y4,−2x4 y6,−2x10 y10 ( )c. 4x6 y4,−x6 y4,3y4x6 b.  3x6 , −5 − x6 y4  ( )d. 3x6 y 4 ,−4x3 y 2 ,−12x9 y8 y4 x6 y4 , 8 Check your answers in the pretest using the correction key at the end of this module.If your score is 13 or 14, scan the material as you review the missed item/s. You may skipthe activities following the pretest and proceed to the posttest. If your score is 15, you mayjust scan the material then proceed to the next module. If your score is below 13, study thewhole module patiently then proceed to the posttest. Answer Key on page 4

What you will doLesson 1: Terms In the previous lesson, you learned that a term is a part of an algebraic expressionindicated as a symbol, product or quotient of coefficients. Terms are parts of an algebraicexpression separated by plus sign (+) or minus sign (-). In this lesson, you will learn toclassify similar and dissimilar terms. Exploration In the expression 2xy, 2 is the numerical coefficient of xy, and x and y are the literalcoefficients of 2. What is the operation between the numerical coefficient and literalcoefficients? The operation used between the numerical and literal coefficients is__________. In the expression − xy , −1 is the numerical coefficient of x and y, and x and y are 55the literal coefficients of −1 . What is the operation involved between the numerical and 5literal coefficients? The operation used between the numerical and literal coefficients is__________.But, what is the operation used between –xy and 5? __________ In the expression 2xy, the operation used between the numerical and literalcoefficients is multiplication. The expression can be read as the product of 2, x, and y. In theexpression − xy , the operation used between the numerical and literal coefficients is also 5multiplication. It can also be read as the product of −1 , x, and y. The expression can also 5be treated as the quotient of –xy and 5 where the operation division is used between –xyand 5. Each of the given expressions is a single term. 5

Activity 1 Classifying TermsLet the following icons stand for the given variables. = x2 = y2 = z2 =x =y =z Every set of pictures in the table on page 6 is represented mathematically using thevariables shown above. Let the operation between the pictures be multiplication.Set of Pictures Algebraic Representation1. z2yx22. xy2z3. x2y2z4. x2zy5. xz2y6. x2zy27. zxy28. z2yxAre there sets of pictures that contain the same pictures? __________ 6

If there are, how are they represented? __________Are the variables in the representations the same? __________Exploration The sets of pictures containing the same pictures represent similar terms while thesets of pictures containing different pictures represent dissimilar terms. Examples ofsimilar terms are the sets of pictures in item #3 and item #6 , which are mathematically represented by x2y2z and x2zy2. Can yougive another two sets of pictures that represent similar terms? __________ The commutative property of real numbers tells us that the order of the addendsor factors does not affect the result. Do you know why xz2y and z2yx are called similarterms? ___________________________________________________________________What can you say about their literal coefficients and their corresponding exponents?_________________________________________________________________________Do the sets of pictures in item #4 and item #5represent similar terms? __________Why or why not? ___________________________________________________________How are these terms called? __________________________________________________Look at these terms 2mn, -4mn, 6mn, do the terms have the same literal coefficients? ____Do they have the same numerical coefficients? __________. Did you know? The numerical coefficients of terms do not affect the similarity of those terms. Onlythe literal coefficients can determine the similarity or dissimilarity of terms. Hence, the terms2mn, -4mn, and 6mn are similar terms. While the terms -5x, 2xy, and -3y2 are not similarterms. They are called dissimilar terms. 7

Furthermore, in classifying algebraic expressions, only the distinct terms should becounted. If there are similar terms, they should be combined.Try ThisConsider the following terms. Write the terms that are similar in column.-2x2y y2x 4yx -6x2 3yx26xy -2x2y2 10x2 4x2y2 3x23xy2 4yx2 -2xy -10y2x x2y2 Remember that similar terms have the same literal coefficient. The phrase ‘the sameliteral coefficient/s’ implies the sameness of exponents of the literal coefficients or variables.So, your groupings must be like these: -2x2y 6xy 3xy2 -2x2y2 10x2 4yx2 4yx Y2x 4x2y2 -6x2 3yx2 -2xy -10y2x x2y2 3x2 Have you done it correctly? Look at the terms in the same column. Take note of theliteral coefficients. You cannot combine the terms in the first column with the terms in thesecond column. They are dissimilar terms. Also the terms in the third, fourth, and fifthcolumns have different literal coefficients.Self-check 1A. From the given set of terms, put similar terms in the same column.4ab2 6ab -4a2 -7b2 2a2b-2a2 -2b2 a2b -10ba 11b2-4a2b -5ab2 10a2 2b2a -15ab Answer Key on page 8

Lesson 2: The Base and Exponent in a Term ‘Math In Action’ In a computer, information is read in units called “bits” and “bytes”. A bit is like an on-off switch and is read by the computer as 1 (on) or 0 (off). A byte is a group of 8 bits, put together to represent one unit of data such as a letter, digit, or a special character. Each byte, therefore, can represent 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 or 256 different characters.Did you know? A product in which the factors are the same is called a power. We can write2 • 2 • 2 • 2 • 2 •2 •2 •2 as 28. The number 8 is called the exponent, and 2 is called thebase. The exponent tells how many times the base is used as a factor. Similarly, we canwrite a •a • a = a3. Here the exponent is 3 and the base is 2. When the base in anexpression is written with exponents higher than 1, we say that the expression is written inexponential notation. For example, bn, can be read as the ‘nth power of b’, or simply ‘b tothe nth’, or ‘b to the n’, or ‘b raised to the n’. We may also read b2 as ‘b squared’ or ‘thesecond power of b’. If the exponent of the base is 1, it may be omitted. For example, in the expression 2b,2 and b are the bases, where 2 is the numerical coefficient of b and b is the literal coefficientof 2. Each base has an exponent of 1. Usually, the base being referred to in algebra is theliteral coefficient. Also, if the numerical coefficient of a term is 1, it may be omitted. Thisalgebraic term y2 means 1y2.Example 1: What is the meaning of each expression?1. 23 23 means 2 • 2 • 22. n4 n4 means n • n • n • n3. 9b3 9b3 means 3 • 3 • b • b • b4. (x+2)3 (x+2)3 means (x+2) (x+2) (x+2)5. [2–(x+y)]2 [2–(x+y)]2 means [2–(x+y)] [2–(x+y)] 9

Example 2: Write each in exponential notation. 1. 7 • 7 • 7 • 7 = 74 2. 2 • 2 • 2 • n • n • n = 23n3 or 8n3 3. 10 • 10 • b • b • b • b = 102b4 or 2252b4 4. (a - 1) (a - 1) (a - 1) (a - 1) (a - 1) = (a – 1)5 5. {(a-1) - 2b} {(a-1) - 2b} {(a-1) - 2b} = {(a-1) - 2b}3Self-check 2Write each in exponential notation and indicate the base and exponent of the result. Factor Form Exponential Base Exponent1. 3 • 3 • 3 • 3 • 3 Notation2. b • b • b • b • b • b3. (2y)(2y)(2y)(2y)4. (z/2) (z/2) (z/2) (z/2)5. (b+c)(b+c)(b+c) Answer Key on pageLesson 3 Operations on Terms Did you know? Classifying terms as similar and dissimilar is very useful in doing operations becauseonly similar terms can be combined through addition and subtraction. We cannot combinedissimilar terms. To add or subtract similar terms, add or subtract their numericalcoefficients following the laws of signed numbers, then copy the common literal coefficientsof the given terms. The result is expressed as the sum or difference of the numericalcoefficients multiplied by the common literal coefficients. 10

Activity 1: Addition of Terms How do we add terms? Let us consider the table of equivalence and examplesbelow. Let the following icons stand for the given variables and constants. Variables Constants= x2 = x = -2= y2 = y= z2 = z =6 = 4 = -4 = 2 = -6Use these representations; study how addition of terms is performed.Illustrative Example1: Add the following:+ - 4xy2 + - 2xy2 - 6xy2 11

Illustrative Example #2 6x2yz2 + + -4x2yz2 2x2yz2 In the first column, the pictures representing the variables in the addends are thesame as the pictures in the sum. Does it mean that the sum of similar terms is also similar tothe result? __________ In item #1, how is the sum –6xy2 obtained? _________________________________ Why is the numerical coefficient in the sum –6 and not 6? _____________________ Addition of terms requires the application of the rules on how to add integers. If theintegers to be added have like signs, add their absolute values then affix their common signlike in this example: - 4xy2 + - 2xy2 - 6xy2 If the integers to be added have unlike signs, find the difference of their absolutevalues, then affix the sign of the integer having the greater absolute value as in thisexample: 6x2yz2 + -4x2yz2 2x2yz2 Are the literal coefficients of the addends the same as the literal coefficients of thesum? ____________________________________________________________________ Finally, how do we add similar terms? _____________________________________ 12

Try ThisFind the sum of the following terms.1. -6x2yz, 4x2yz, 3x2yz2. 2ab, -8ab, 5ab, -6ab, 4ab3. 3x2y, -9x2y, 6yx2, -x2y, 4yx2 It is easier to determine whether terms are similar if these are arranged in column.Did you get all answers correctly? _____________________________________________Answers: 1) x2yz 2) –3ab 3) 3x2yActivity 2: Subtraction of Terms How do we subtract terms? Let us also consider the table of equivalence used in adding terms in analyzing theexamples that follow: Illustrative Example #1 4xy2 _ _ - 2xy2 6xy2 13

Illustrative Example #2 - 2x2yz2 _ _ - 6x2yz2 4x2yz2 In the first column, the pictures representing the variables are the same in theminuend, in the subtrahend and in the difference. Does it mean that the difference of similarterms also contains exactly the same literal coefficient? ____________________________ In item #1, how is the difference between 4xy2 and -2xy2 obtained?_________________________________________________________________________ Why is the numerical coefficient in the sum 6 and not - 6? _____________________ Subtraction of monomials requires the application of the rules on how to subtractintegers. In subtracting integers, change the sign of the subtrahend and proceed as inaddition of integers like in these examples 4xy2 4xy2 _ - 2xy2 + + (-) 2xy2 6xy2and -2x2yz2 - 2x2yz2 _ -6x2yz2 + + (-)6x2yz2 4x2yz2 Are the literal coefficients of the terms being subtracted the same as the literalcoefficients of their difference? ________________________________________________ Finally, how do we subtract similar monomials?_________________________________________________________________________ 14

Analyze further the examples below. 1. 4a2 – (+6a) Change the sign of the subtrahend and = 4a2 + (-6a2) proceed to addition of signed numbers. = -2a2 Bring down the literal coefficient. 2. 4a2b – (-6a2b) Change the sign of the subtrahend, then = 4a2b + (+6a2b) add. = 10a2b Bring down the literal coefficient.Try ThisFind the difference between the given terms in each item.1. 6mn 2. -36y 3. –3a2b 4. 7x2yz3 8mn 10y - 6a2b -3x2yz3Have you answered the items correctly? __________Compare your answers with the following: 1) –2mn; 2) – 46y; 3) 3a2b; and 4) 10x2yz3.Self-check 3 A. Find the sum of the terms in each of the items. Terms Answer 1. 8ab, -11ab, 6ab 1. 2. 6xy, 8xy, -16xy, 5xy 2. 3. -5mn, -3mn, 9mn, -5mn 3. 4. bc, -8bc, 3bc, 5bc, -2bc 4. 5. -35ax, -16ax, 45ax, -12ax, 12ax 5. 15

B. Find the difference between the terms in each item.Subtract the second term from the first term. Terms Answer1. -19y, -30y 1.2. 36xy, 45xy 2.3. -4ac, 3ac 3.4. -48a2b, -32a2b 4.5. -37x2, -48x2 5. Answer Key on pageLesson 4 Simplifying Terms Using the Laws of Exponents Exploration If the same number is multiplied to itself for a number of times, we can write it in ashorter way. The number is used as a base and the number of times the number or base isused as a factor becomes the exponent. If you use 3 five times as a factor as in 3 · 3 · 3 · 3· 3, it could be written as 35. In 35, 5 is the exponent indicating the number of times 3 is usedas a factor. Similarly, x · x · x · x can be written as x4. This manner of writing numbers iscalled the exponential notation.Activity 1: Multiplying Powers with Like Bases Multiplying Powers For any rational number n, and for all whole numbers a and b, (na)(nb) = na+b. 16

Study these examples. 1. 2 · 2 · 2 · 2 = 24 2. a · a· a · b · b = a3b2Why is 2 · 2 · 2 · 2 equal to 24? ________________________________________________Why is 4 used as the exponent of 2? ___________________________________________How many times is the base 2 used as a factor? __________ Is there any exponent of 2when used as a factor? __________ If ever there were, what is the exponent and what didyou do to get 4 as the exponent of the base 2 in the product?_________________________________________________________________________Why is a · a · a · b · b equal to a3b2 and not equal to (ab)5? _________________________Why are 3 and 2 used as exponents of a and b, respectively? _______________________Why can’t we add the exponents of a and b to get (ab)5? ___________________________ The law on multiplying powers is used in these examples. Illustrative example #1 Illustrative example #2 a2 · a4 = (a · a)(a · a · a · a) 3x3y2 · 5xy3 = 3 · 5 · x3 · x · y2· y3 = a2 + 4 = 15x3 + 1y2 + 3 = a6 = 15x4y5 In example #1, the base a with 2 as the exponent is multiplied with the samebase a with 4 as exponent.What do you notice with the exponents of base a? ________________________________Are the exponents 2 and 4 added to get a6? _____________________________________ In example #2, there is a numerical coefficient in each factor. As you can see, 3 and5 are multiplied to get 15. Are the exponents of x in the two factors added to get x4?_________________________________________________________________________How did you get y5 in the product? _____________________________________________ Error Analysis: Find and correct each error in the following exercises. a. (3x2)(2x5) = 6x(2)(5) = 6x10 b. (x5)(x)(x2) = x5+2 = x7Challenge: Write each of the following as a power of 2. 17

a. 16 b. 43 c. 82 d. (43)(8)(16)Activity 2 Raising a Power to a PowerWe can use the meaning of an exponent to simplify an expression like (32)4. (32)4 = (32) (32) (32) (32) = 32+2+2+2 Using the rule for multiplying powers with like bases = 38Notice that we get the same result if we multiply the exponents. (32)4 = 3(2)(4) = 38In general, we can state the following rule for raising a power to a power.For any rational number n, and any whole numbers a and b, (am)n = amn Study the following examples:Example 1: (xy)3 = (xy)(xy)(xy) = (x · x · x)(y · y · y) = x3y3Example 2: (4x3y2)2 = (4x3y2)(4x3y2) = (4·4)(x3 · x3)(y2 · y2) or 4(1)(2)x(3)(2)y(2)(2) = 42x6y4 or 42x6y4 = 16x6y4 or 16x6y4 Look at illustrative example #1. The exponent 3 in expression (xy) tells how manytimes each base is used as a factor. In Illustrative example #2, the numerical coefficient 4 isalso squared because it is also a base within the grouping symbol.Thus,(4·4)(x3 · x3)(y2 · y2) or 4(1)(2)x(3)(2)y(2)(2) may be used to get 16x2y2. 18

Try ThisSimplify each of the following using the laws of exponents discussed above. Given Answer1. 3x · 4x22. (3a2b)33. (-2a3b2)(3a3b5)4. (-2a2b3c)35. (2m2n)( -4mn)( 3m3n2)Check your answers using this answer key.1. 12x3 2. 27a6b3 3. –6a6b7 4. –8a6b9c3 5. –24m6n4 Notice that in items 1, 3, and 5, numerical coefficients and literal coefficients are justmultiplied to get the numerical coefficients and literal coefficients of the results. However, initems 2 and 4, powers of the numerical coefficients and literal coefficients are obtained toget the numerical coefficients and the literal coefficients of the results. If you did not get theanswers correctly, go back to the examples given in this lessonSelf-check 4Multiplication Simplify each of the following Factors Product1. 3xy2 · 6x3y3 1.2. (3x2y2)3 2.3. -3x · 6x2 · 2x3 3.4. (-4x2)2 4.5. 7a2b3c · 3abc 5. 19

Answer Key on page 32Critical Thinking: Is (a + b)m = am + bm true for all numbers? If yes, justify your answer. If no, give a counterexample.Activity 3: Dividing Powers with Like Bases The following suggests a rule for simplifying expressions in the form am . an 35 = 3 · 3 · 3 · 3 · 3 = 3 · 3 = 32 33 3 · 3 · 3 Notice that we can subtract the exponents to find the exponent of the quotient. Dividing powers For any rational number a except 0, and for all whole numbers m and n, am = am-n anDefinition of a Negative Exponent For any rational number a except 0, and for all whole numbers m, a-m = 1 . amDefinition For any rational number a except 0, a0 = 1. Study the following examples as to show how the laws of exponents work in division. Example #1 1. x6 = x · x · x · x · x · x = x6-2 = x4 x2 x · x 20

2. 12a5b6c3 = 2 · 2 · 3a5b6c3 = 2231-1a5-3b6-4c3-1 = 4a2b2c2 3a3b4c 3a3b4c In x6 , x6 is the dividend and x2 is the divisor. x2 In division, we cancel the same factors in both dividend and divisor. If the dividend isy7 and the divisor is y5, what do you think is the answer? y7 = y • y • y • y • y • y • y = y2 y5 y • y • y • y • y Look at example 2. Both the dividend and divisor have numerical coefficientsother than 1. So, twelve is written in factor form so that it will be divided by 3 following therule or law of exponent to get the quotient 4. Look at how the same factors are cancelledapplying the law of dividing powers with the same bases. The exponents are subtracted,aren’t they? Could you give the quotient to this expression − 16m6n5 It should be done like ? 8m3n3this: = -(24-3m6-3n5-3) = -2m3n2 Analyze further the following examples: 1. x3 = x · x · x =1 x6 x · x · x · x · x · x x3 Also, x3 = x3 – 6 = x—3 = 1 x6 x3 2. -10m6n4 = -2 · 5 m · m · m · m · m · m · n · n · n · n_____ 5m7n6 5 m·m·m·m·m·m·m·n·n·n·n·n·n = -2 = -2_ m · n · n mn2 Therefore, -10m6n4 = -2m6 – 7n4 – 6 = -2m-1n-2 5m7n6 = -2_ mn2 3. 8a5b4 = 2 · 2 · 2 · a · a · a · a · a · b · b · b · b = 2(1)(1) = 2 21

4a5b4 2 · 2 · a · a · a · a · a · b · b · b · b or = 23-2a5 – 5b4 – 4 = 21a0b0 (Definition 2) =2·1·1 =2 Try This Simplify each of the following using the laws of exponents. Given Answer 1. 8a8 2a5 2. -12x5y3 6x3y2 3. 6m5n4 2m6n7 4. x4y3 x4y3 5. 2a3 · 4b2 8a3b2 If you have followed the given examples, you could have done those items abovecorrectly. Check your answer and review if you made a mistake.1. 4a3 2. -2x2y 3. _3 4. 1 5. 1 mn3 In Items 4 and 5, the exponents of the same bases in both divisor and dividend areequal, so, if you subtract the exponents of the same bases, you get a zero exponent. 22

For any base (except 0) raised to a zero exponent is always 1.Critical Thinking:How are the following items below simplified to get the indicated answers?1.  x 2 = x2 2.  a2 4 = a8 3.  2a2  = 4a4 y y2 b3 b12 3b3 9b6Error Analysis: Elaine wrote in her Math journal “The square of any number is alwaysgreater than the number”. Find a counterexample to show that Elaine’s statement isincorrect.Mathematical Reasoning: Square any number, and then double the result. Is youranswer always, sometimes, or never greater than the result of doubling the number, thensquaring it? Justify your answer.Self-check 4Do the indicated operation.DivisionSimplify the following monomials using the laws of exponents in division. 1. 2. 3. 4. 5.Expression 3x5 b6c5d2 -16x3y6 15a6y7 (3x3/4y4)3 Answer x2 b4c7d3 8x5y3 5a6y7 Answer Key on page 32 23

Lesson 5 Scientific NotationRead the following article carefully. It is about ‘Math in Action’. The distance from Earth to the North Star is about 10 000 000000 000 000 000 meters. The thickness of a soap bubble is about0.0000001 meter. It is easy to make errors when working withnumbers involving many zeros. If an extra zero is included, theresulting number is ten times larger or ten times smaller. To prevent this type of error and to make it easier to work withvery large numbers and very small numbers, we can write thesenumbers in a form called scientific notation. Using scientific notation,we can write a number as the product of a power of 10 and a numbergreater or equal to 1, but less than 10. In scientific notation, thedistance to the North Star is 1.0 x 1019 meters and the thickness of asoap bubble is about 1.0 x 10-7 meter. The numbers 10 000 000 000000 000000 and 0.0000001 are expressed using the standardnotation. Can you still remember how to express multiplication phrase in exponential form?The expression 42 means 4 · 4 = 16, 53 means 5 · 5 · 5 = 125. How about 103? Its base is10 so you multiply 10 by itself three times → 10 · 10 · 10 = 1000.1. How do you express 10 000 using 10 as the base? __________; 100 000?______________2. How about 1 ? __________, 1 ? __________, 1 ? __________100 1000 10000 In item #1, using 10 as a base, 10 000 can be written as 104, while 100 000 can alsobe written as 105. In item #2, 1 is written as 1 or 10-2 100 102 1 = 1 or 10-3 1000 103 24

1 = 1 or 10-4 10000 104 In the examples, the base is 10. Unlike in a6, the base is a. The expression a-6 alsomeans 1 . a6Study ThisActivity 1: Computing the Product of a Number and a Power of 10 Try to find the products of the following. a) 24 x 10 c) 24 x 103 e) 24.567 x 102 f) 24.567 x 103 b) 24 x 102 d) 24.567 x 10 Let us look at the answers. Is there any pattern? __________ What pattern can youderive from the products? ________________________________________ a) 24 x 10 = 240 d) 24.567 x 10 = 245.67 b) 24 x 102 = 2,400 e) 24.567 x 102 = 2456.7 c) 24 x 103 = 24,000 f) 24.567 x 103 = 24567 Do you know how each product is obtained? To multiply a number by any positivepower of 10, you simply move the decimal point to the right by as many places as theexponent of 10.Activity 2: Computing the Quotient of a Number and a Power of 10 Try to get the quotients of the following. Each number is divided by a positive powerof 10. a) 165 ÷ 10 d) 25.8 ÷ 10 b) 165 ÷ 102 e) 25.8 ÷ 102 c) 165 ÷ 103 f) 25.8 ÷ 103 How did you do it? ____________________________________________ Do yousee a pattern? __________ If there is any, what is it?_________________________________________________________ Is the pattern you 25

derived from dividing the numbers the same as the pattern you derived from themultiplication of the numbers? ___________________________ The quotient can be obtained by moving the decimal point to the left as many placesas the exponent of 10.So, the answers are the following:a) 165 ÷ 10 = 16.5 Move 1 place to the left.b) 165 ÷ 102 = 1.65 Move 2 places to the left.c) 165 ÷ 103 = .165 How many places to the left?d) 25.8 ÷ 10 = 2.58 How many places to the left?e) 25.8 ÷ 102 = .258 How many places to the left?f) 25.8 ÷ 103 = .0258 You move the decimal point 3 places to the left; there’s no other digit, so you add a cipher before the last non-zero digit from the right then put the decimal point. The procedures learned from the multiplication and division of numbers by thepowers of ten help you understand how to write numbers in scientific notation. Thistechnique of writing numbers is based on the powers of 10. It is very useful in expressingvery large or very small numbers in a way that is easier to read. Did you know? Consider the following information:1. The earth’s distance from the sun is about 149 590 000 km. This number can be rewritten as 1.4959 x 100 000 000 or 1.4959 x 108 km in scientific notation.2. A light year is the distance that light travels in a year. It is approximately 9 460 800 000 000 km. It can be rewritten as 9.408 x 100 000 000 or 9.408 x 108 in scientific notation.3. The diameter of a red blood cell is about 0.00075 cm. It can be rewritten as 7.5 x 1 or 7.5 x 10-4 cm in scientific notation. 10000 Can you see the equivalence of these numbers? __________1) 149 590 000 = 1.4959 x 100 000 000 = 1.4959 x 1082) 940 800 000 000 = 9.408 x 100 000 000 = 9.408 x 108 26

3) 0.00075 = 7.5 × 1 = 7.5 ×10−4 10000Study the table. Standard Notation Scientific Notation 1. 149 590 000 1. 1.4959 x 108 2. 940 800 000 000 2. 9.408 x 108 3. 0.00075 3. 7.5 x 10-4 Look at the location of the decimal point in the scientific notations of the numbersgiven above. Can you describe where the decimal point is located?______________________________________________________________ How is the exponent of the factor 10 obtained? ___________________You should have discovered that the decimal point in the scientific notation of a number islocated just after the first non-zero digit from the left, which is known as its standard locationin scientific notation. Also, the exponent of 10 depends on how many times you move thedecimal from its given location to its standard location.Try ThisA. Write each number in standard notation. Given Number Standard Notation1. 35.345 x 1032. 35.345 ÷ 1023. 5.35 ÷ 103B. Express the following information in scientific notation. Information Scientific Notation1. The earth’s diameter is 12 760 km. 27

2. The speed of light is 279 600 km/s.Check your answers.A. Standard Notation1. 35 345 Just move three places to the right.2. .35345 Just move two places to the left.3. .00535 Just move two places to the left.Why move the decimal point to the left for item numbers 2 and 3?B. Scientific Notation 1. 1.276 x 104 2. 2.796 x 105 Did you get all the answers? That’s very good! You are now ready to express thosebig numbers and small numbers in scientific notation.Self-check 5 Express each number in scientific notation.Standard Notation Scientific Notation1) 56,700,0002) 876,0003) 0.001344) 0.03720 Answer Key on page 32 28

Let’s summarize Kinds of TermsSimilar terms are terms with the same literal coefficients.Dissimilar terms are terms with different literal coefficients. Similar terms in an algebraic expression may be combined in to a single termby adding or subtracting their numerical coefficients, as indicated by the signs,keeping the identical literal factors. Exponential Notation Any number expressed in the form bn is in exponential notation where bis the base and n is the exponent. Exponent is a symbol or a number at the upper right hand corner of avariable or constant. It tells how many times a base is used as a factor. Base is the repeated factor in a power. Addition and Subtraction of Similar Monomials To add or subtract similar terms, add or subtract their numerical coefficientsfollowing the laws of integers and copy their common literal coefficients. Simplification of Terms Expressed as Product or Quotient To simplify terms expressed as product, multiply the numerical coefficients of thefactors following laws of integers and multiply the literal coefficients of the factorsfollowing the rules of exponents (na)(nb) = na+b and (am)n = amn.To simplify terms expressed as quotient, divide the numerical coefficients of thenumerator and denominator following the laws of integers and divide the literalcoefficients of the numerator and denominator following the rules of exponents indivision am = am−n and  a n = an . an b bn Scientific NotationA number is expressed in scientific notation when it is in the form a x 10n, 29

where 1 ≤ a < 10 and n is an integer.What to do after (Posttest)Direction: Choose the letter of the correct answer.1. Which of the following sets contains similar terms?a. –3x2y, 6xy2, x2y2, -9x2y c. –a2b, 8ba2, 6a2b, -5ba2b. xy2, -7xy, 2x2y2, -5xy2 d. abc, 3bca, 6a2bc, -8a2c2. In the expression 12m2, m is the coefficient of __________.a. 12 b. 12m2 c. 12m d. m23. What value of the variable x makes the statement (x0 = 1) false?a. negative integer b. fraction c. positive integer d. zero4. What is the sum of the terms 8x, -4x, and -6x?a. -4x b. -2x c. 2x d. 4x d. -10x35. What is the product of -2x3 and 5x.?a. 10x4 b. 10x3 c. -10x46. What is the difference between -8mn and -5mn?a. -13mn b. -3mn c. 13mn d. 3mn d. 3a9b77. What is the quotient if 24a6b5 is divided by -8a3b2?a. -3a2b2 b. -3a3b3 c. 3a3b38. What is 345 600 in scientific notation?a. 3.456 x 102 b. 3.456 x 103 c. 3.456 x 104 d. 3.456 x 1059. What is 1 if it is written in the power of 10? 10000a. 10-2 b. 10-3 c. 10-4 d. 1/10410. Which of the following is true about the expression -5x3? a. x is the literal coefficient of 5x3. b. –5 is the numerical coefficient of x3. 30

c. 5 is the numerical coefficient of -5x3.d. 3 is the common exponent of –5 and x.11. What is the standard notation of 2.35 x 102?a. 2.35 b. 23.5 c. 235 d. 2 35012. When the exponent of 10 in the scientific notation of a number is negative, it means thatthe numbera. is less than 1. c. is equal to 1.b. is greater than 1. d. could not be determined.13. If 4.506 is written in scientific notation, what is the exponent of 10?a. –1 b. 0 c. 1 d. 214. What do you call the repeated factor in a power?a. term b. product c. exponent d. base15. When (22x3)3 is simplified, what will be the numerical coefficient of the result?a. 64 b. 32 c. 8 d. 4 Answer Key on page 32 31

Answer Key Pretest page 3 1. d 4. b 7. b 10. a 13. b 2. b 5. a 8. c 11. a 14. d 3. c 6. d 9. c 12. c 15. c Lesson 1 Self-Check 1 page 84ab2 -2a2 -4a2b 6ab -2b2-5ab2 -7b22ab2 -4a2 a2b 10ab 11b2 10a2 2a2b -15ab Lesson 2 Self-Check 2 page 10Factor Form Exponential Notation Base Exponent 3 51. 3 x 3 x 3 x 3 x 3 35 b 62. b x b x b x b x b x b b6 43. (2y)(2y)(2y)(2y) (2y)4 (2y) 44. (z/2) (z/2) (z/2) (z/2) (z/2)4 (z/2) 35. (b+c)(b+c)(b+c) (b+c)3 (b+c)1. 3ab Lesson 3 Self-Check 3 5. –6ax1. 11y A. Addition page 15 5. 11x2 2. 3xy 3. –4mn 4. -bc B. Subtraction page 16 2. –9xy 3. –3ac 4. –16a2b Lesson 4 Self-Check 4 Multiplication page 191. 18x4y5 2. 27x6y6 3. –36x6 4. 16x4 5. 21a3b4c2 1. 3x3 5. 27x9/64y12 Division page 23 2. b2/c2d 3. –2y3/x2 4. 3 Lesson 5 Self-Check 5 page 28 1. 5.67 x 107 2. 8.76 x 105 3. 1.34 x 10-3 4. 3.72 x 10-2 Posttest page 30 1. c 6. b 11. c 2. c 7. b 12. a 3. d 8. d 13. b 4. b 9. c 14. d 5. c 10. b 15. a 32

END OF MODULE BIBLIOGRAPHYCariño, Isidro D. (1999). Elemtary algebra for high school: Integrating desirable Filipino values II . Pasig City: Anvil Publishing Inc.Charles, Randall I. and . (1996). Secondary math: An integrated approach focus on algebra. USA: Addison-Wesley Publishing Company.Dugopolski, Mark. (2001). Algebra for college students. 2nd ed. Singapore: McGraw-Hill Book Co.Malaborbor, Pastor B. et al. (2002). Elementary algebra for the basic education curriculum. Metro Manila: Diamond Offset Press.Smith, S.A. et al. _____. Algebra 1. New York, NY: Prentice-Hall. 33