5.4 The Distributive Property Objective:​
to apply the Distributive Property to rewrite algebraic expressions Vocabulary: ➢equivalent expressions ­ expressions that have the same value. ★ The ​
Distributive Property​
states that to multiply a sum or difference by a number, multiply each term inside the parentheses by the number outside the parentheses. Symbols
a(b + c) = ab + ac
a(b − c) = ab − ac Examples 4(6 + 2) = 4(6) + 4(2) 3(7 − 5) = 3(7) − 3(5) The expressions 2(x + 2) and 2x + 4 are equivalent expressions. No matter what x is, these expressions have the same value. Examples: Use the Distributive Property to solve a) 5(− 9 + 11) 5(− 9 + 11) = 5(− 9) + 5(11)
Expand using the Distributive Property = − 45 + 55
Multiply = 10
Add b) 7(10 − 5) 7(10 − 5) = 7(10) − 7(5)
Expand using the Distributive Property = 70 − 35
Multiply = 35
Subtract c) (12 − 8)9 d) 6(a + 4) e)
(m + 3n)8 f)
− 3(y − 10) g)
1
2 (w − 4) h) A sports club rents dirt bikes for $37.50 each. Find the total cost for the club to rent 20 bikes. Justify your answer by using the Distributive Property. 20($30.00 + $7.00 + $0.50)
Guided practice: p.378, #1 ­ 5 HW: p. 379 ­ 382, #1 ­ 24, and 40 ­ 46 even Guided practice: 1. ­57 2. ­10x ­ 20y 3. 15 g − 2 4. 160ft; 25(6 + 0.4) = 25 • 6 + 25 • 0.4 5. You can find the sum of the length and width and then multiply by two, 2(l + w). You can also find the sum of twice the length and twice the width, (2l + 2w) . Example answer key: c) 36 d) 6(a + 4) = 6a + 6(4) = 6a + 24 e) 8m + 24n f)
− 3y + 30 g) 12 w − 2 h) $750; 20($30.00 + $7.00 + $0.50) = 20(30) + 20(7) + 20(0.5) = 600 + 140 + 10 = 750