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Objective- To use the distributive property to simplify variable expressions.

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## Objective- To use the distributive property to simplify variable expressions.

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**Objective- To use the distributive property to simplify**variable expressions. Distributive Property a(b + c) = ab + ac Order of Operations Distributive Property 6(3 + 5) 6(3 + 5) 6(3) + 6(5) 6(8) 48 18 + 30 48 Why distribute when order of operations is faster ?**Use the distributive property to simplify.**1) 3(x + 7) 6) x(a + m) ax + mx 3x + 21 2) 2(a + 4) 7) 4(3 + r) 2a + 8 12 + 4r 3) 7(8 + m) 8) 2(x + 8) 2x + 16 56 + 7m 4) 3(4 + a) 9) 7(2m + 3y + 4) 12 + 3a 14m + 21y + 28 5) (3 + k)5 10) (6 + 2y + a)3 15 + 5k 18 + 6y + 3a**Use the distributive property to simplify.**1) 4(y + 7) 6) a(c + d) 4y + 28 ac + ad 2) 3(b + 6) 7) 8(3 + r) 3b + 18 24 + 8r 3) 5(9 + m) 8) 4(x + y + 1) 45 + 5m 4x + 4y + 4 4) 5(4 + a) 9) 5(2m + 3 + t) 20 + 5a 10m + 15 + 5t 5) (7 + k)6 10) (11 + 2y)+3y 42 + 6k 11 + 5y**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)**Geometric Model for Distributive Property**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)**Geometric Model for Distributive Property**4 x 9 Two ways to find the total area. Width by total length Sum of smaller rectangles = 9(4 + x) 9(4) + 9(x)**Factoring**Find the missing factor. 1) 2) 3) 4) 5)**Find the GCF of the following mentally.**1) 2) 3) 4) Factoring Greatest Common Factor GCF -**Factor the following expression.**1) 3) 2) 4) Factoring One type involves the Distributive Property in reverse.**Factoring**One type involves the Distributive Property in reverse. Factor the following expression. 5) 7) 6) 8)**Like Terms**Like terms - variable terms that differ only in their coefficients. Unlike Terms Like Terms 7x 3y 7x 3x 5y y 5y 10xy 2yx 2a 3ab**Simplify by combining like terms.**1) 7x + 4y + 2x + y 5) 4k + (2j) + 6k + j + 3j 10k 9x + 5y 2) 3m + 10n + 4m + 1 6) 10 + 4x + 3y + 17x 21x 7m + 10n + 1 + 3y + 10 7) 3) 7x + 3y 7x + 3y 4) 6x + (5x) + 2x + 3 8) 13x + 3**Simplify the expression using the Distributive**Property and then combining like terms. 3) 1) 2) 4)**Simplify each variable expression.**5) 7(x + 4) + 2x 8) 3(b + 2) + 6b 7x + 28 + 2x 3b + 6 + 6b 9x + 28 9b + 6 6) 5x + 3(x + 1) 9) 2(3m + 1) + 4m 5x + 3x + 3 6m + 2 + 4m 8x + 3 10m + 2 7) a + 2(4 + a ) + 1 10) 3(k + m) + 5(k + 2m) + 5k + 10m a + 8 + 2a + 1 3k + 3m 3a + 9 8k + 13m