Distributive Property a(b + c) = ab + ac Example: 2(x + 3) = 2x + 6 (b + c)a = ba + ca Example: (x + 7)3 = 3x + 21 a(b c) = ab ac Example: 5(x 2) = 5x 10 (b c)a = ba ca Example: (x 3)6 = 6x 18 57
Distributive Property The Distributive Property can be used to eliminate parentheses, so you can then combine like terms. For example: 3(4x 6) 3(4x) 3(6) 12x 18 58
26 Simplify 4(7x + 5) using the distributive property. A 7x + 20 B 28x + 5 Answer C 28x + 20 59
27 Simplify 6(2x + 4) using the distributive property. A 12x + 4 B 12x + 24 Answer C 12x + 4 D 8x + 10 60
28 Simplify 3(5m 8) using the distributive property. A 35m 8 B 15m + 24 Answer C 15m 24 D 8m 11 61
29 ) 4(x + 6) is the same as 4 + 4(6). True False Answer 62
30 Use the distributive property to rewrite the expression without parentheses. 2(x + 5) A 2x + 5 Answer B 2x + 10 C x + 10 D 7x 63
31 Use the distributive property to rewrite the expression without parentheses. (x 6)3 A 3x 6 Answer B 3x 18 C x 18 D 15x 64
32 Use the distributive property to rewrite the expression without parentheses. 0.6(3.1x + 17) A 186x + 102 B 1.86x + 17 Answer C 1.86x + 10.2 D .631x + .617 65
33 Use the distributive property to rewrite the expression without parentheses. 0.5(10x 15) A 5x 75 Answer 10x 7.5 B C 5x 7.5 D 5x 15 66
34 Use the distributive property to rewrite the expression without parentheses. 1.3(6x + 49) A 78x + 637 Answer B 7.8x + 63.7 C 7.8x + 49 D 1.36x + 1.349 67
Real Life Situation You went to the supermarket and bought 4 bottles of orange soda and 5 bottles of purple soda. Each bottle cost $2. How much did you pay in all? Use the distributive property to show two different ways to solve the problem. $2 (4 orange sodas + 5 purple sodas) $2 x 9 sodas $18 OR ($2 x 4 orange sodas) + ($2 x 5 purple sodas) $8 + $10 $18 68
Real Life Situation You bought 10 packages of gum. Each package has 5 sticks of gum. You gave away 7 packages to each of your friends. How many sticks of gum do you have left? Use the distributive property to show two different ways to solve the problem. 5 sticks x (10 packages 7 packages) 5 sticks x 3 packages 15 sticks of gum OR (5 sticks x 10 packages) (5 sticks x 7 packages) 50 sticks of gum 35 sticks of gum 15 sticks of gum 69
35 Canoes rent for $29 per day. Which expression can be used to find the cost in dollars of renting 6 canoes for a day? A (6 + 20) + (6 + 9) B (6 + 20) x (6 + 9) Answer C (6 x 20) + (6 x 9) D (6 x 20) x (6 x 9) 70
36 A restaurant owner bought 5 large bags of flour for $45 each and 5 large bags of sugar for $25 each. The expression 5 x 45 + 5 x 25 gives the total cost in dollars of the flour and sugar. Which is another way to write this expression? A 5 + (45 + 25) Answer B 5 x (45 + 25) C 5 + (45 x 5) + 25 D 5 x (45 + 5) x 25 71
37 Tickets for the amusement park cost $36 each. Which expression can be used to find the cost in dollars of 8 tickets for the amusement park? A (8 x 30) + (8 x 6) B (8 + 30) + (8 + 6) Answer C (8 x 30) x (8 x 6) D (8 + 30) x (8 + 6) 72
Like Terms Math Practice Return to Table of Contents 73
Like Terms Like Terms : Terms in an expression that have the same variable(s) raised to the same power Like Terms NOT Like Terms 6x and 2x 6x and y 5y and 8y 5y and 8 4z and 7z 4y and z 74
38 Identify all of the terms like 5y. A 5 B 4z C 18y Answer D 8y E 1y 75
39 Identify all of the terms like 8x. 5x A 4z B C 8y Answer D 8 E 10x 76
40 Identify all of the terms like 8xy. 5x A 4zy B C 3xy Answer D 8y E 10xy 77
41 Identify all of the terms like 2y. A 51y B 2w C 3y Answer D 2x E 10y 78
42 Identify all of the terms like 14z. 5x A 2z B 3y C Answer D 2x 10x E 79
43 Identify all of the terms like 0.75z. 75x A 75z B 3y C Answer D 2x 10z E 80
2 3 x 44 Identify all of the terms like 5x A 2z B 3y C Answer D 2x 10z E 81
1 4 z 45 Identify all of the terms like 5x A B 2x 3z C 2z D Answer 10x E 82
Combining Like Terms Simplify by combining like terms 6x + 3x MP6: Attend to precision. Math Practice (6 + 3)x Emphasize the addition/subtraction of the 9x coefficients w/ the degree of the variable remaining the same. Notice when combining like terms you add/subtract the coefficients but the variable remains the same. 83
Combining Like Terms Simplify by combining like terms 4 + 5(x + 3) MP6: Attend to precision. Math Practice 4 + 5(x) + 5(3) Emphasize the addition/subtraction of the 4 + 5x + 15 coefficients w/ the degree of the variable remaining the same. 5x + 19 Notice when combining like terms you add/subtract the coefficients but the variable remains the same. 84
Combining Like Terms Simplify by combining like terms 7y 4y (7 4)y MP6: Attend to precision. Math Practice 3y Emphasize the addition/subtraction of the coefficients w/ the degree of the variable remaining the same. Notice when combining like terms you add/subtract the coefficients but the variable remains the same. 85
46 Simplify the expression 8x + 9x. A x B 17x Answer C x D cannot be simplified 86
47 Simplify the expression 7y 5y. A 2y B 12y Answer C 2y D cannot be simplified 87
48 Simplify the expression 6 + 2x + 12x. A 6 + 10x B 20x Answer C 6 + 14x D cannot be simplified 88
49 Simplify the expression 7x + 7y. A 14xy B 14x Answer C 14y D cannot be simplified 89
50 ) 8x + 3x is the same as 11x. True False Answer 90
51 ) 7x + 7y is the same as 14xy. True False Answer 91
52 ) 12y + 4y is the same as 8y. True False Answer 92
53 ) 3 + y + 5 is the same as 2y. True False Answer 93
54 ) 5y 3y is the same as 2y. True False Answer 94
55 ) 7x + 3(x 4) is the same as 10x 12. True False Answer 95
56 ) 7 + 5(x + 2) is the same as 5x + 9. True False Answer 96
57 ) 4 + 6(x 3) is the same as 6x 14. True False Answer 97
58 ) 3x + 2y + 4x + 12 is the same as 9xy + 12. True False Answer 98
59 The lengths of the sides of home plate in baseball are represented by the expressions in the accompanying figure. Which expression represents the perimeter of the home plate? Answer yz y y A 5xyz B x + yz C 2x + 3yz x x D 2x + 2y + yz 99
60 Find an expression for the perimeter of the octagon. x +24 A x+2 6x + 24 B Answer x x+3 24x C 7 7 30x D x+3 x+2 x 100
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