Extra Practice Chapter 3. Topics Include: Exponents Algebra Terms Simplify Polynomials Distributive Property

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1 Extra Practice Chapter Topics Include: Exponents Algebra Terms Simplify Polynomials Distributive Property

2 Practice: Work With Exponents BLM What is the base of each power? a) 5 b) c) ( ) d) e) f).1. Write the exponent for each power in question 1.. Which expressions are equal to? A B C 1 D 6. Which expression in question is written as a power? 5. Which expressions are equal to? A B C D Which expression in question 5 is written in expanded form? 7. Write each expression as a power. a) b) 9 9 c) d) ( 7) ( 7) ( 7) ( 7) ( 7) e) ( 1.) ( 1.) ( 1.) ( 1.) f) Write each power in expanded form, then evaluate. a) b) 5 c) ( ) d) e) 1 9. Evaluate. f) 0. a) 6 b) 7 c) d) ( ) 6 e) 1 1 f) Use the correct order of operations to evaluate each expression. a) + b) 6 6 c) ( + 5) d) ( + 5 ) 1 e) 6 f) Evaluate each expression for the given values of the variables. a) x x = b) x + 5 x = c) r r r = 6 d) t t t = e) m + m m = f) x y x = 7, y = 5 BLM..1 Practice: Work With Exponents Copyright 006 McGraw-Hill Ryerson Limited.

3 Practice: Discover the Exponent Laws BLM Write each expression in expanded form. Then write as a single power. a) 7 7 b) 5 c) 5 5 d) e) ( ) ( ) f) ( 1) ( 1) ( 1) g) h) 1 1. Evaluate each expression in question 1.. Write each expression in expanded form. Then write as a single power. a) b) c) d) 8 5 e) ( 9) 7 ( 9) 6 f) g) ( 0.) ( 0.) h) 5. Evaluate each expression in question. 5. Write each expression in expanded form. Then, write as a single power. a) ( ) b) (6 ) c) ( ) d) [( ) ] e) [( 1) 8 ] 6 f) [( 1) 5 ] 7 g) (0. ) h) 5 6. Evaluate each expression in question Use the exponent laws to simplify each expression. Then, evaluate. a) 5 b) c) d) e) ( ) f) ( ) 8 g) (0. ) 5 h) [( ) ] [( ) ] 5 8. Simplify. a) b 5 b b) p p c) w 5 w d) x 8 x e) (m 5 ) f) (k ) k g) g 5 g 5 g 7 h) (a 6 ) (a 5 ) 9. Simplify. a) a b 5 ab b) m n m n c) p 6 q 5 p q d) 6xy y e) (gh ) f) k m (k ) g) (g 5 h ) gh 6 h) 6bd bd ( bd) BLM..1 Practice: Discover the Exponent Laws Copyright 006 McGraw-Hill Ryerson Limited.

4 Practice: Communicate With Algebra BLM For each term, identify the coefficient and the variable. a) x b) 5p c) m n d) g h e) y 5 f) p q 5 g) ab h) 0.6r s. The expression x + 5 is a: A monomial B binomial C trinomial D term. The expression 1m n is a: A monomial B binomial C trinomial D term. The expression a b + ab + b is a: A monomial B binomial C trinomial D term 5. Classify each polynomial by type. a) x + 1 b) p p + c) b d d) 6 + gh 5 e) y 5 y + y f) x y + g) ab b h) 6p q 6. What is the degree of each term in question 5? 7. The degree of 5m n + mn + 1 is: A 1 B C D 8. What is the degree of each polynomial? a) 6a + b b) 5b c) x + x 1 d) m m + m e) p q f) x y + xy g) a 5 b 7b h) m n m n + mn 9. Which algebraic expression matches this phrase: a number increased by 6 is 8 A 6x = 8 B x + 8 = 6 C x + 6 = 8 x D 8 6 = 10. Write an equation for each phrase. a) double a number is 1 b) a number decreased by 6 is 5 c) one third of a number is d) triple a number, increased by 1 is Maggie earns $5 per hour when she babysits 1 child. She earns $8 per hour when she babysits children. Let x represent the number of hours she babysits 1 child and y represent the number of hours she babysits children. Which expression represents her total earnings? A 5x 8y B x + y C 5x + 8y D x y 1. Evaluate each expression for the given values of the variables. a) x x = b) y + y = 7 c) r r + 1 r = 6 d) a b a =, b = 1 e) p + p p = f) x y x =, y = 1 BLM..1 Practice: Communicate With Algebra Copyright 006 McGraw-Hill Ryerson Limited.

5 Practice: Collect Like Terms BLM Which polynomial contains a term like xy? A xy x y B x + xy C x + y xy D x + y +. Are the terms in each pair like or unlike? a) 5a and a b) x and x c) p and p d) ab and ab e) b and b f) 6a b and a b g) 9pq and p q h) x y and x y. Write one like term and one unlike term for each. a) p b) a c) k d) x e) mn f) ab g) pq h) b d. Is it possible to simplify each expression? How do you know? a) 8a + a b) 5m + n c) p + p d) t 7t e) x f) v v + v g) 6c c c h) r + r Simplify each expression. a) p + p b) 7g g c) a 8a d) 5x x e) 6q + q f) y + 5y g) u + u u h) 7b b b 6. Collect like terms. Then, simplify. a) b + b + 1 b) p 7 p + c) 1 + y + + y d) 5 x 1 x e) 6a b + b + a f) 7r + + r r 1 g) 9s s + 5t s h) g h + 5h + g h 7. Simplify. a) + v + 5v 10 b) 7a b a b c) 8k k 5k + + k d) x x + 8x + 5x e) 1 m 8 m + m f) 6y + y + 10 y 6 y g) 5 + h + h + h h h) p + q p + p 7q 8. Simplify. a) a + 6b + b + a b) x + xy + y + 5x xy y c) m m m + m d) x + xy + y x + xy y 9. The length of a rectangle is times the width of the rectangle. Let x represent the width of the rectangle. a) Write an expression to represent the length of the rectangle. b) Write a simplified expression for the perimeter of the rectangle. c) Suppose the width is 6 cm. Find the perimeter of the rectangle. BLM.5.1 Practice: Collect Like Terms Copyright 006 McGraw-Hill Ryerson Limited.

6 Practice: Add and Subtract Polynomials BLM Which expression represents the result of simplifying (x ) + (x + 1)? A 6x B 6x + C 5x + D 5x. Remove brackets and collect like terms. Then, simplify. a) (x + ) + (x + 5) b) (y 5) + (y + 9) c) (5m + 1) + (m + ) d) ( d) + (d 1) e) (v ) + (6 v) f) (k + ) + ( k) + (6k 1) g) (p + ) + (p ) + (8 p) h) ( r) + ( + 5r) + (r 1). Write the opposite of each expression. a) b) 5 c) p d) x e) m + f) b 1 g) x + x h) 6 y. Which expression represents the result of simplifying (x 1) (x + 1)? A 5x + B x C 5x D x 5. Add the opposite. Then, simplify. a) (d ) (d + 1) b) (x ) (x + ) c) (p + 5) (p + ) d) (8 m) (m ) e) (a ) (5 a) f) (z + 7) ( z) g) (p + 1) (p ) h) (5 b) (6 + b) 6. Simplify. a) (6k ) + (k + ) b) (n + ) + (n 5) c) (a + 1) (a + ) d) (5 m) + (m 1) e) (b 6) ( 5b) + (b + ) f) (x + ) (1 x) (5 + x) g) (g + 1) + (g 7) ( g) h) (1 b) + ( + b) (b 8) 7. Simplify. a) (x + x + 1) + (x + ) b) (a + b 6) + (a b + ) c) (m + m + 1) + (m + m 6) d) (5n + mn m) + (m 5mn + n) 8. A rectangle has length x + 1 and width x +. a) Write a simplified expression for the perimeter of the rectangle. b) Find the perimeter of the rectangle when x = Three artists contributed to a coffee-table book. They each chose to be paid a different way. Royalty Artist Fixed Rate ($) ($ per n books sold) Ayesha 1000 n Jorge 5n Ioana 000 a) Write an expression for the total earnings for each artist. b) Write a simplified expression for the total amount paid to Ayesha, Jorge, and Ioana. BLM.6.1 Practice: Add and Subtract Polynomials Copyright 006 McGraw-Hill Ryerson Limited.

7 Practice: The Distributive Property BLM Model each expression with algebra tiles. Then, simplify each expression. a) 5(x + ) b) (x + ) c) x(x + ) d) x(x + 5). Which expression is equal to 6(x )? A 6x B 6x + C x D 6x. Use the distributive property to expand. a) (g + ) b) (a + 5) c) 6(x ) d) 5(b 1) e) ( r) f) 7(q + ) g) (6 t) h) ( w 5) 5. Expand. a) b(b + 1) b) m(m + ) c) x(x ) d) a(a + 1) e) r(r + 5) f) q(q + ) g) k(6 k) h) w(w 5) 6. Expand. a) p(p + ) b) s(s + ) c) x(x 1) d) 6b(b + 1) e) r( 5r + ) f) y(y 7) g) 5c(8 c) h) w(w 1) 7. Expand. a) (d + ) b) (k + 1) c) (w ) 5 d) (u 1) ( ) e) (q + 5) 6 f) ( p + ) ( ) g) (5 z)(z) h) (6w )( w) 8. Expand. a) (x + x ) b) (m m + 5) c) (b b ) d) 5c(c 6c 1) e) h( h ) f) (n + n + )( ) g) (5t t)( t) h) (w + w 5)(w) 9. Expand and simplify. a) (b + ) + 5(b + ) b) (p ) + 6(p + 1) c) 5(m + 5) + (m 7) d) (d ) (d + ) 10. Expand and simplify. a) [b + (b + 1)] b) [(a + ) ] c) 5[s (s + )] d) [ (6 t) + 5t] BLM.7. Practice: The Distributive Property Copyright 006 McGraw-Hill Ryerson Limited.

8 Chapter Review BLM.CR.1... (page 1).1 Build Algebraic Models Using Concrete Materials, pages Use algebra tiles. Model each algebraic expression. a) x + b) x c) x + x d) x + x +. One face of a cube has area 6 cm. a) What is the side length of the cube? b) Find the volume of the cube.. Work With Exponents, pages Evaluate. a) 5 b) 8 c) d) ( ) e) ( 1) 10 f) BLM.CR.1 Chapter Review. Evaluate. Use the correct order of operations. a) + b) 7 7 c) 9 d) 5 5 e) ( + ) f) ( + ) 5. A scientist studying a type of bacteria notices that the population doubles every 0 minutes. The initial population is 500. a) Copy and complete the table. Time (min) Population b) Construct a graph of population versus time. Connect the points with a smooth curve.. Discover the Exponent Laws, pages Write as a single power. Then, evaluate. a) b) c) ( ) 9 d) ( ) e) 7 5 ( ) f) [( 6) ] [( 6) ] 7. Simplify. a) b 6 b b) g g 8 g 7 c) (a 5 ) (a ) d) m 5 n m n e) p 7 q p q f) 8b d bd ( bd). Communicate With Algebra, pages Identify the coefficient and the variable for each term. a) 7m b) x 5 c) 7 m n d) gh 9. Classify each expression as a monomial, binomial, trinomial, or polynomial. a) a a + 1 b) x 5x + x c) 6m n 5 d) h + 6 e) 1x f) x y + 8 Copyright 006 McGraw-Hill Ryerson Limited.

9 10. State the degree of each term. a) 8b b) x y c) mn d) 6r 6 s 11. What is the degree of each polynomial? a) 5a + b b) 7b 6 c) x + x 1 d) 8m m + m.5 Collect Like Terms, pages Classify each pair of terms as like or unlike. a) a and a b) 6x and x c) 1p and p d) a b and 6a b 1. Simplify each expression. a) b + 7g 5b 8g b) x + y + 5y 7x c) 6q + u + u + q + u + u u d) 10 m 7 m + m e) v + v + 6 v 9 v f) 7 + h + h 5 + 6h + + h.6 Add and Subtract Polynomials, pages Simplify. a) (6k ) + (k + ) b) (a + 1) (a + ) c) (b 6) ( 5b) + (b + ) d) (g + 1) + (g 7) ( g) e) (x + x + 1) + (x + ) BLM.CR.1... (page ) f) (m + m + 1) (m + m 6) 15. The length of the Cheungs back yard is double its width. a) Write an expression for the perimeter of their back yard. b) The width of their back yard is 9 m. What is its perimeter?.7 The Distributive Property, pages Expand. a) 5(x + ) b) (b + ) c) w(w + 1) d) q(q + ) e) c(6 c) f) p(p 1) g) 5(a a ) h) d(d d 1) 17. Expand and simplify. a) (x + ) + (x + 1) b) (m + ) + (m 7) c) (d ) 5(d + ) d) 5[b + (b + 1)] e) [(a + ) ] f) [ ( t) + t] BLM.CR.1 Chapter Review Copyright 006 McGraw-Hill Ryerson Limited.

10 BLM Answers BLM..1 Practice: Work With Exponents 1. a) 5 b) c) ( ) d) e) f).1. a) b) c) d) e) f). B; D. 5. C: D a) 6 7 b) 9 c) 0. d) ( 7) 5 e) ( 1.) f) ( ) 5 8. a) ; 81 b) 5 5 5; 15 c) ( ) ( ); d) ( ); e) ( )( ) ( ) ; 1 f) ; a) 16 b) 18 c) d) 6 e) 1 f) ( ) a) 5 b) 10 c) 9 d) 9 e) f) 11. a) 8 b) c) 18 d) 8 e) 8 f) BLM..1 Practice: Discover the Exponent Laws 1. a) ; 7 6 b) ; 8 c) 5 5 5; 5 d) ; 9 e) ( ) ( ) ( ) ( ) ( ); ( ) 5 f) ( 1) ( 1) ( 1) ( 1) ( 1) ( 1); ( 1) 6 g) ; h) ( ) ( ) ( ) ( ) ; ( ). a) b) 6561 c) 15 d) e) f) 1 g) h) a) ; b) ; c) ; d) e) f) g) ; ( ) ( 9) ( 9) ( 9) ( 9) ( 9) ( 9) ( 9) ; ( 9) 1 ( 9) ( 9) ( 9) ( 9) ( 9) ( 9) ; ( 0.) ( 0.) ( 0.) ( 0.) ; ( 0.) ( 0.) ( ) ( ) ( ) ( ) ( ) h) ( ) ( ) ( ) ; ( ). a) 6 b) 5 c) d) 16 e) 9 f) 0.01 g) 0.07 h) 9 5. a) ( ) ( ) ( ) ( ); 8 b) (6 ) (6 ); 6 c) ( ) ( ); 6 d) ( ) ( ) ( ) ; ( ) 1 e) ( 1) 8 ( 1) 8 ( 1) 8 ( 1) 8 ( 1) 8 ( 1) 8 ; ( 1) 8 f) ( 1) 5 ( 1) 5 ( 1) 5 ( 1) 5 ( 1) 5 ( 1) 5 ( 1) 5 ; ( 1) 5 g) (0. ) (0. ); 0. h) ( ) ( ) ; ( ) a) 56 b) 196 c) 79 d) 096 e) 1 f) 1 g) h) a) ; 16 b) 8 1 ; 8 c) 9 ; 81 d) 6 ; 16 e) 11 ; 08 f) ; 7 g) 0. 1 ; 0. h) ( ) ; a) b 8 b) p 5 c) w d) x e) m 10 f) k 8 g) g h) a 8 9. a) a 5 b 8 b) m 5 n 7 c) p q d) xy e) g h 1 f) 8k 6 m g) g 9 h) b d

11 BLM Answers BLM..1 Practice: Communicate With Algebra 1. a) coefficient: ; variable: x b) coefficient: 5; variable: p c) coefficient: ; variable: m n d) coefficient: 1; variable: g h e) coefficient: ; variable: y 5 f) coefficient: 1; variable: p q 5 g) coefficient: ; variable: ab h) coefficient: 0.6; variable: r s. B: binomial. A: monomial and D: term. C: trinomial 5. a) binomial b) trinomial c) monomial d) binomial e) four-term polynomial f) trinomial g) binomial h) monomial 6. a) 1 b) c) 5 d) 6 e) 5 f) g) h) 6 7. D: 8. a) b) c) d) e) 7 f) g) 6 h) 7 9. C 10. a) x = 1 b) x 6 = 5 c) x = d) x + 1 = C 1. a) 5 b) c) 1 d) 7 e) 1 f) 1 BLM.5.1 Practice: Collect Like Terms 1. B: x + xy. a) like b) unlike c) like d) like e) unlike f) like g) unlike h) unlike. a) like: 7p; unlike: x b) like: a ; unlike: a c) like: 5k ; unlike: k d) like: x; unlike: p e) like: mn ; unlike: m n f) like: ab; unlike: a g) like: pq ; unlike: p q h) like: b d ; unlike: bd. a) yes; both terms have the variable a b) no; the terms have different variables c) yes; both terms have the variable p d) yes; both terms have the variable t e) no; the terms have different variables f) yes; all terms have the variable v g) yes; all terms have the variable c h) no; the terms do not all have the same variables 5. a) p b) g c) 6a d) x e) 7q f) 9y g) u h) b 6. a) b b + + 1; b + b) p p 7 + ; p c) y + y; 5 +y d) 5 1 x x; x e) 6a + a b + b; 8a + b f) 7r + r r + 1; 9r + 1 g) 9s s s + 5t; s + 5t h) g + g h + 5h h; g + h 7. a) 6v 6 b) 6a 5b c) 7k + 5 d) 10x + x e) m f) 5y + g) 7 + 7h h) 6p 5q 8. a) a + 7b 6 b) 9x + xy y c) m m + d) 5xy + y 9. a) L = x b) P = 6x c) 6cm BLM.6.1 Practice: Add and Subtract Polynomials 1. D: 5x. a) x + 8 b) y + c) 7m + d) d e) v + f) k + 5 g) 10 h) 6 + 6r. a) b) 5 c) p d) x e) m f) b + 1 g) x x + h) 6 + y. B: x 5. a) d b) x 7 c) p + d) 10 5m e) a 7 f) z + g) h) 1 6b 6. a) 8k b) n c) a 1 d) m e) 7b f) x g) 5g + h) 1 7. a) x + x + 5 b) 6a + b c) 5m + 5m + 6 d) 6n mn m 8. a) P = 10x + 6 b) a) Ayesha: n; Jorge: 5n; Ioana: 000 b) Total = n BLM.7. Practice: The Distributive Property. a) 5x + 10 b) 8x + 1 c) x + x d) x + 10x. D: 6x. a) g + 1 b) a + 10 c) 6x 18 d) 5b 5 e) 1 r f) 7q 1 g) 1 + t h) w a) b + b b) m + m

12 BLM Answers c) x x d) a + a e) r + 5r f) q + q g) 6k k h) w 5w 6. a) p + 1p b) s + s c) 8x x d) 18b + 6b e) 5r r f) y + 7y g) 0c 10c h) 6w + w 7. a) d + 6 b) k + c) 5w 10 d) u + e) 1q + 0 f) p 8 g) 15z z h) 18w + 1w 8. a) x + x 1 b) m 6m + 10 c) b + 8b + 1 d) 5c 0c 5c e) 1h + h f) n 8n 6 g) 5t + t h) w + 8w 0w 9. a) 7b + 6 b) 9p c) m 9 d) 5d 10. a) 16b + 1 b) 6a + 16 c) 15s 10 d) 6 + 1t BLM.CR.1 Chapter Review. a) 6 cm b) 16 cm. a) 15 b) 56 c) 81 8 d) 16 e) 1 f) ( ) 7. a) 97 b) c) 9 8 d) ( ) e) 5 f) 9 5. a) 5 Time (min) Population a) 8 ; 6 b) 6 1 ; 6 c) ; 7 d) 5 ; 65 e) ; 16 f) ( 6) 1 ; 6 7. a) b 9 b) g c) a 7 d) m 7 n 5 e) p f) b d 8. a) coefficient: 7; variable m b) coefficient: ; variable x 5 c) coefficient: 7 ; variable m n d) coefficient: 1; variable gh 9. a) trinomial b) polynomial c) monomial d) binomial e) monomial f) trinomial 10. a) b) 7 c) d) a) b) 6 c) d) 1. a) unlike b) like c) like d) unlike 1. a) b g b) x + 6y c) 7q + 9u d) + m e) 5v f) + 11h 1. a) 8k b) a 1 c) 7b d) 5g + e) x + x + 5 f) m m a) P = 6x b) 5 m 16. a) 5x + 15 b) b + 8 c) w + w d) q + q e) 18c 1c f) p + p g) 5a + 0a + 10 h) d 6d d 17. a) 5x + 11 b) m 9 c) 6d 7 d) 15b + 10 e) 6a 10 f) + 0t b)