Lesson 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 + 5) 6(8) 6(3) + 6(5) 48 18 + 30 48 Why distribute when order of operations is faster ? Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series Algebra 1 by James Wenk © 2003 published by TEACHINGpoint

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

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

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

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

Simplify the following. 1) 10 - 4(x - 5) - 8 4) 5x - 4(7x - 9) - 11 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series