1. 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

2. 1. 4x 2 + 8x + 21 2. -7x 2 + 17x – 23 3. 6x 3 + 4x + 1 4. 7x 3 + 8x 2 + 3x – 13 5. 13x 2 + 8x + 17 6. -2x 2 + 11x + 18 7. -6x 3 + x 2 – x – 7 8. 8x 3 – 2x 2 + 15 9. 9x 2 – 4x + 63 10. 11x 3 + 24x + 1 11. 2x 2 + 2x – 4 12. -12x 9 + 8x 6 – 3 13. 7x 3 – 16x + 19 14. -x 8 – 67x + 8 15. -16x 2 + 34x – 97 16. -6x 2 – 29x + 19 17. -22x 3 – 13x 2 + x 18. -x 6 – 34x 4 + 26 19. 8x 2 – 15x + 65 20. 2x + 1 21. 5xy 2 + 11x – 8y 2 22. 3x 2 + 65xy + 5y 2 – 9x 23. 2.2x 2 +.26xy – 13.7y 2 24. 4x 3 – 4x 2 + 8x – 4

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

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

6. 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!

7. 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!)

8. (2x + 2)(3x + 1) Mult.3x+1 2x +2 Break each expression into terms.

9. (2x + 2)(3x + 1) Mult.3x+1 2x +2 Now we multiply! 6x 2

10. (2x + 2)(3x + 1) Mult.3x+1 2x +2 Now we multiply! 6x 2 + 2x

11. (2x + 2)(3x + 1) Mult.3x+1 2x +2 Now we multiply! 6x 2 + 2x + 6x

12. (2x + 2)(3x + 1) Mult.3x+1 2x +2 Now we multiply! 6x 2 + 2x + 6x+ 2

13. (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

14. (2x + 1)(3x – 5) 6x 2 – 10x + 3x – 5 6x 2 – 7x – 5 Mult. +3x – 5 +2x + 1 +6x 2 – 10x + 3x– 5

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

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

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

18. 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

19. 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

20. 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

21. (3x + 4)(5x – 2) First: +3x ∙ +5x = +15x 2

22. (3x + 4)(5x – 2) First: +3x ∙ +5x = +15x 2 Outer: +3x ∙ - 2 = - 6x

23. (3x + 4)(5x – 2) First: +3x ∙ +5x = +15x 2 Outer: +3x ∙ - 2 = - 6x Inner: +4 ∙ +5x = +20x

24. (3x + 4)(5x – 2) First: +3x ∙ +5x = +15x 2 Outer: +3x ∙ - 2 = - 6x Inner: +4 ∙ +5x = +20x Last: +4 ∙ - 2 = - 8

25. (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 2 + 14x – 8

26. (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!