 Distributive Property ◦ a(b+c) = ab + ac5(3x+1) = 15x + 5 ◦ a(b-c) = ab – ac5(3x-1) = 15x - 5 ◦ (b+c)a = ab + ac(3x+1)5 = 15x + 5 ◦ (b-c)a = ab – ac(3x-1)5 = 15x - 5  Simplify ◦ 34(102) =  34(100+2) =  34(100) + 34(2) =  =  3468  Your Practice ◦ 24(98) = ◦ 24(90) + 24(8) = ◦ = ◦ 2352

 Useful when shopping  c = $2.95n ◦ n = 8  c = 2.95(8)  = 3(8) -.05(8)  =  = $23.60  4(.99) = ◦ 4(1.00) – 4(.01) = ◦ = ◦ $3.96

 Simplify  2(5x+3) ◦ 2(5x) + 2(3) ◦ 10x + 6  ( c)(3) ◦ 3(.4) + 3(1.1c) ◦ c  Your practice ◦ Simplify ◦ 2(3-7t)  2(3) – 2(7t)  6 – 14t

 Same rules, just a sign change  -(6x+4) ◦ -6x – 4  (9-4n)(-4) ◦ n  Don’t confuse (9-4n)-4  No parenthesis means add or subtract  Your practice ◦ -3(-4x + 7) ◦ 12x - 21

 Like Terms  Same letter and exponents ◦ 3x and -2x ◦ -5x 2 and 9x 2 ◦ xy and –xy ◦ -7x 2 y 3 and 15x 2 y 3  Not Like Terms  Different letters and/or exponents ◦ 8x and 7y ◦ 5y and 2y 2 ◦ 4y and 5xy ◦ x 2 y and xy 2

 Add or subtract coefficients ◦ Number in front of a letter  Simplify ◦ Determine if like terms or not  If not, then just leave alone ◦ 3x 2 + 5x 2  Keep letters and exponents the same  (3+5)x 2  8x 2 ◦ 12k 2 + 8k 2  (12+8)k 2  20k 2

 Your Practice  Simplify ◦ 13q – 30q  (13-30)q  -17q

 Write expression for “3 times the quantity x minus 5” ◦ Quantity means ( )  3(x-5)  “-2 time the quantity t plus 7” ◦ -2(t+7)  Your practice ◦ Write expression ◦ Product of 14 and the quantity 8 plus w  14(8+w)