1 5 1 6 Rules of signed numbers

1. 5 -1. 6 Rules of signed numbers https: //www. youtube. com/ watch? v=Vw 7 CUBX 8 DU 4

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) 2) 2(a + 4) 7) 4(3 + r) 3) 7(8 + m) 8) 2(x + 8) 4) 3(4 + a) 9) 7(2 m + 3 y + 4) 5) (3 + k)5 10) (6 + 2 y + a)3

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) 2) 3(b + 6) 7) 8(3 + r) 3) 5(9 + m) 8) 4(x + y + 1) 4) 5(4 + a) 9) 5(2 m + 3 + t) 5) (7 + k)6 10) (11 + 2 y)+3 y

Use the distributive property to simplify. 1) 4(y + 7) 6) a(c + d) 2) 3(b - 6) 7) 8(3 + r) 3) 5(9 +2 m) 8) 4(x - y + 1) 4) 5(4 + a) 9) 5(2 m + 3 + t) 5) (7 - 4 k)6 10) (11 + 2 y)3 y

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)

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 2) 3 m + 10 n + 4 m + 1 6) 10 + 4 x + 3 y + 17 x 3) 7 x + 3 y 7) 4) 6 x + (5 x) + 2 x + 3 8)

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