Simplify by combining like terms: 1. (5x 3 – 3x) + (8x 3 + 4x) = 2. (4y 3 + 8xy) – (3xy + 9y 3 )= 3. (5x 3 – 2y 3 ) – (5y 3 + 6x 3 )= 13x 3 + x -5y 3 +

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Simplify by combining like terms: 1. (5x 3 – 3x) + (8x 3 + 4x) = 2. (4y 3 + 8xy) – (3xy + 9y 3 )= 3. (5x 3 – 2y 3 ) – (5y 3 + 6x 3 )= 13x 3 + x -5y 3 + 5xy -x 3 – 7y 3

1. 4x 2 + 8x x x – x 3 + 4x x 3 + 8x 2 + 3x – x 2 + 8x x x x 3 + x 2 – x – x 3 – 2x x 2 – 4x x x x 2 + 2x – x 9 + 8x 6 – x 3 – 16x x 8 – 67x x x – x 2 – 29x x 3 – 13x 2 + x 18. -x 6 – 34x x 2 – 15x x xy x – 8y x xy + 5y 2 – 9x x xy – 13.7y x 3 – 4x 2 + 8x – 4

Distributive Property – Review!!! 3(x + 5) = 3x + 15 We will need that same concept to multiply polynomials. 3(2x 2 + 4x + 3)= 6x 2 We will distribute the outside term to everything on the inside. + 12x+ 9

4(3x 2 – 2x + 1)= 12x 2 – 8x + 4 2x(2x 2 + x + 5)= 4x 3 + 2x x 4 ∙ 3x 2 4 ∙ –2x 4 ∙ 1 2x ∙ 2x 2 2x ∙ x 2x ∙ 5 12x 2 –8x +4 4x 3 +2x 2 +10x

3x 2 (2x 3 + 2x 2 – 2x) = 6x 5 + 6x 4 – 6x 3 3x 2 ∙ 2x 3 3x 2 ∙ 2x 2 3x 2 ∙ – 2x Notice the negative! (2x + 2)(3x + 1) This gets a little more complicated! We now have to distribute TWO terms!

Distributing this gets confusing!!!! (2x + 2)(3x + 1) I will show you two ways to multiply this: Expansion Boxes and FOIL. You decide which works for you! (I like Expansion Boxes!)

(2x + 2)(3x + 1) Mult.3x+1 2x +2 Break each expression into terms.

(2x + 2)(3x + 1) Mult.3x+1 2x +2 Now we multiply! 6x 2

(2x + 2)(3x + 1) Mult.3x+1 2x +2 Now we multiply! 6x 2 + 2x

(2x + 2)(3x + 1) Mult.3x+1 2x +2 Now we multiply! 6x 2 + 2x + 6x

(2x + 2)(3x + 1) Mult.3x+1 2x +2 Now we multiply! 6x 2 + 2x + 6x+ 2

(2x + 2)(3x + 1) Mult.3x+1 2x +2 Now we combine terms! 6x 2 + 2x + 6x+ 2 6x 2 + 2x + 6x + 2 6x 2 + 8x + 2

(2x + 1)(3x – 5) 6x 2 – 10x + 3x – 5 6x 2 – 7x – 5 Mult. +3x – 5 +2x x 2 – 10x + 3x– 5

(x + 5)(-x – 2) -x 2 – 2x – 5x – 10 -x 2 – 7x – 10 Mult. -x – 2 x + 5 -x 2 – 2x – 5x– 10

FOIL is an acronym for: (2x + 2)(3x + 1) First Outer Inner Last First: +2x ∙ +3x = +6x 2

FOIL is an acronym for: (2x + 2)(3x + 1) First Outer Inner Last First: +2x ∙ +3x = +6x 2 Outer: +2x ∙ +1 = +2x

FOIL is an acronym for: (2x + 2)(3x + 1) First Outer Inner Last First: +2x ∙ +3x = +6x 2 Outer: +2x ∙ +1 = +2x Inner: +2 ∙ +3x = +6x

FOIL is an acronym for: (2x + 2)(3x + 1) First Outer Inner Last First: +2x ∙ +3x = +6x 2 Outer: +2x ∙ +1 = +2x Inner: +2 ∙ +3x = +6x Last: +2 ∙ +1 = +2

FOIL is an acronym for: (2x + 2)(3x + 1) First Outer Inner Last First: +2x ∙ +3x = +6x 2 Outer: +2x ∙ +1 = +2x Inner: +2 ∙ +3x = +6x Last: +2 ∙ +1 = +2 Now we combine! 6x 2 + 2x + 6x + 2 6x 2 + 8x + 2

(3x + 4)(5x – 2) First: +3x ∙ +5x = +15x 2

(3x + 4)(5x – 2) First: +3x ∙ +5x = +15x 2 Outer: +3x ∙ - 2 = - 6x

(3x + 4)(5x – 2) First: +3x ∙ +5x = +15x 2 Outer: +3x ∙ - 2 = - 6x Inner: +4 ∙ +5x = +20x

(3x + 4)(5x – 2) First: +3x ∙ +5x = +15x 2 Outer: +3x ∙ - 2 = - 6x Inner: +4 ∙ +5x = +20x Last: +4 ∙ - 2 = - 8

(3x + 4)(5x + 2) First: +3x ∙ +5x = +15x 2 Outer: +3x ∙ - 2 = - 6x Inner: +4 ∙ +5x = +20x Last: +4 ∙ - 2 = - 8 Combine: 15x 2 – 6x + 20x – 8 15x x – 8

(2x + 1)(4x – 3) Combine: 8x 2 – 6x + 4x – 3 8x 2 – 2x – 3 Mult. 4x – 3 2x + 1 8x 2 – 6x + 4x– 3 First: +2x ∙ +4x = +8x 2 Outer: +2x ∙ -3 = -6x Inner: +1 ∙ +4x = +4x Last: +1 ∙ -3 = -3 Combine: 8x 2 – 6x + 4x – 3 8x 2 – 2x – 3 Same Answer!