Objective To use the distributive property to simplify

Objective- To use the distributive property to simplify variable expressions. Distributive Property a(b + c) = ab + ac Order of Operations 6(3 + 5) 6(8) 48 Distributive Property 6(3 + 5) 6(3) + 6(5) 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 3 x + 21 2) 2(a + 4) 7) 4(3 + r) 2 a + 8 12 + 4 r 3) 7(8 + m) 8) 2(x + 8) 2 x + 16 56 + 7 m 4) 3(4 + a) 9) 7(2 m + 3 y + 4) 12 + 3 a 5) (3 + k)5 15 + 5 k 14 m + 21 y + 28 10) (6 + 2 y + a)3 18 + 6 y + 3 a

Use the distributive property to simplify. 1) 4(y + 7) 6) a(c + d) 4 y + 28 ac + ad 2) 3(b + 6) 7) 8(3 + r) 3 b + 18 24 + 8 r 3) 5(9 + m) 8) 4(x + y + 1) 45 + 5 m 4 x + 4 y + 4 4) 5(4 + a) 9) 5(2 m + 3 + t) 20 + 5 a 10 m + 15 + 5 t 5) (7 + k)6 10) (11 + 2 y)+3 y 42 + 6 k 11 + 5 y

Geometric Model for Distributive Property 3 7 4 Two ways to find the total area. Width by total length 4(3 + 7) Sum of smaller rectangles

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)

Geometric Model for Distributive Property 4 x 9 Two ways to find the total area. Width by total length 9(4 + x) Sum of smaller rectangles = 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) 3) 2) 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 7 x 3 x Unlike Terms 7 x 3 y 5 y 10 xy 2 yx 2 a 3 ab

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

Simplify the expression using the Distributive Property and then combining like terms. 1) 3) 2) 4)

Simplify each variable expression. 5) 7(x + 4) + 2 x 8) 3(b + 2) + 6 b 7 x + 28 + 2 x 9 x + 28 6) 5 x + 3(x + 1) 5 x + 3 8 x + 3 7) a + 2(4 + a ) + 1 a + 8 + 2 a + 1 3 a + 9 3 b + 6 b 9 b + 6 9) 2(3 m + 1) + 4 m 6 m + 2 + 4 m 10 m + 2 10) 3(k + m) + 5(k + 2 m) 3 k + 3 m + 5 k + 10 m 8 k + 13 m