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

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. 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

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)

= 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)

= 9(4 + x) 9(4) + 9(x) 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)

Factoring GCF - Greatest Common Factor Find the GCF of the following mentally. 1) 2) 3) 4)

Factoring One type involves the Distributive Property in reverse. Factor the following expression. 1) 2) 3) 4)

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. Like Terms Unlike Terms 7x 3x 7x 3y 5y y 5y 10xy 2yx 2a 3ab

Simplify by combining like terms. 1) 7x + 4y + 2x + y 5) 4k + (2j) + 6k + j 9x + 5y 10k + 3j 2) 3m + 10n + 4m + 1 6) 10 + 4x + 3y + 17x 7m + 10n + 1 21x + 3y + 10 3) 7x + 3y 7) 7x + 3y 4) 6x + (5x) + 2x + 3 8) 13x + 3

Simplify the expression using the Distributive Property and then combining like terms. 1) 3) 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) a + 8 + 2a + 1 3k + 3m + 5k + 10m 3a + 9 8k + 13m