Exercise Find the following products mentally. 5(20) 100 5(7) 35 5(27) 135

Exercise Find the following products mentally. 3(20) 60 3(3) 9 3(23) 69

Exercise Find the following products mentally. 7(82) 574

Distributive Property For any integers a, b, and c, a(b + c) = ab + ac.

Example 3(2 + 5) = 3 • 2 + 3 • 5 3(7) = 6 + 15 21 = 21

a(b – c) = ab – ac

Example 3(8 − 5) = 3 • 8 − 3 • 5 3(3) = 24 − 15 9 = 9

Example 1 Use the Distributive Property to write an equivalent expression. Then simplify if possible. −5(2 − 7) = −5 • 2 − (−5) • 7 = −10 − (−35) = −10 + 35 = 25

Example 1 Use the Distributive Property to write an equivalent expression. Then simplify if possible. 4(m + n) = 4m + 4n

3(74)

ab + ac = a(b + c)

Example 2 Use the Distributive Property to write an equivalent expression. 4(−8) + 4(32) = 4(−8 + 32)

Example 2 Use the Distributive Property to write an equivalent expression. −3(7) − 3x = −3(7) + (−3)x = −3(7 + x)

Example 3 Write an equivalent expression for (5 + x)y. (5 + x)y =

Exercise Identify the property used for each step in simplifying the following. 6 + 3r + 5 = = 3r + 6 + 5 = 3r + 11

Exercise Identify the property used for each step in simplifying the following. 4n + 2m + 9n = = 4n + 9n + 2m = (4 + 9)n + 2m = 13n + 2m

Exercise Identify the property used for each step in simplifying the following. 2x + 3y − 4x + 8 = = 2x − 4x + 3y + 8 = (2 − 4)x + 3y + 8 = −2x + 3y + 8

Exercise Identify the property used for each step in simplifying the following. 2(h + 3) + h = = 2h + h + 6 = 2h + 1h + 6 = (2 + 1)h + 6 = 3h + 6

Exercise Identify the property used for each step in simplifying the following. (5b + 6) − 2b = (6 + 5b) − 2b = 6 + (5b − 2b) = 6 + (5 − 2)b = 6 + 3b = 3b + 6