1 7 Distributive Property Objective To use the

1: 7 Distributive Property Objective- To use the distributive property to simplify variable expressions. Distributive Property a(b + c) = ab + ac or a(b - c) = ab - ac Order of Operations Distributive Property 6(3 + 5) 6(3) + 6(5) 6(8) 18 + 30 48 48 Why distribute when order of operations is faster ? 1 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Use the distributive property to simplify. 1) 3(x + 7) 6) x(a + m) 3 x + 21 ax + am 2) 2(a - 4) 7) -4(-3 - r) 2 a - 8 12 + 4 r 3) -7(8 - m) 8) 2 x(x - 8) -56 + 7 m 2 x 2 - 16 x 4) 3 a(4 - a) 9) -5 m(2 m + 3) 2 12 a - 3 a -10 m 2 - 15 m 5) (3 - k)5 10) (6 - 2 y)-3 y 15 - 5 k 6 - 5 y Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 2

Geometric Model for Distributive Property 3 7 4 Two ways to find the total area. Width by total length Sum of smaller rectangles 4(3 + 7) 3 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Geometric Model for Distributive Property 3 7 4 4(3) 4(7) Two ways to find the total area. Width by total length 4(3 + 7) Sum of smaller rectangles = 4(3) + 4(7) 4 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Subtracting a Quantity 1) -(x + 6) -x - 6 2) -(2 x - 8) -2 x + 8 3) 10 - (4 m + 3) 10 - 4 m - 3 - 4 m + 7 4) 2(x - 5) - (x - 3) 2 x - 10 - x + 3 x-7 6) -(3 a + 1) -3 a - 1 2 7) -(-3 x + 2 x -7) 2 +3 x - 2 x + 7 8) -12 - (3 y - 8) -12 - 3 y + 8 - 3 y - 4 9) 4(3 k - 5) - (2 k + 9) 12 k - 20 - 2 k - 9 10 k - 29 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 5

Simplify the following. 1) 10 - 4(x - 5) - 8 4) 5 x - 4(7 x - 9) - 11 5 x - 28 x + 36 - 11 10 - 4 x + 20 - 8 - 23 x + 25 - 4 x + 22 2) 6 - 2(5 - x) - (3 x + 7) 6 - 10 + 2 x - 3 x - 7 - x - 11 3) 4 x - 5[2(6 x - 3) - 7] 4 x - 5[12 x - 6 - 7] 4 x - 5[12 x - 13] 4 x - 60 x + 65 -56 x + 65 5) 10 + 3(x - 5) - (2 x - 9) 10 + 3 x - 15 - 2 x + 18 x + 13 6) -4[-(x + 5) - 3(x - 6)] -4[-x + -5 - 3 x + 18] -4[-4 x + 13] 16 x - 52 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 6