1. 5.3 Notes – Add, Subtract, & Multiply Polynomials

2. When you add or subtract variables, you change the coefficient, not the exponent When multiplying variables, you change the coefficient and the exponent 4x + 2x =6x6x 4x  2x = 8x28x2

3. 1. (z 2 + 5z – 7) + (5z 2 – 11z – 6) 6z26z2 – 6z – 13 For #1-3, find the sum or difference.

4. 2. (2a 2 – 8) – (a 3 + 4a 2 – 12a + 4) –a3–a3 – 2a 2 + 12a 2a 2 – 8 – a 3 – 4a 2 + 12a – 4 – 12 For #1-3, find the sum or difference.

5. (8v 4 – 2v 2 + v – 4) – (3v 3 – 12v 2 + 8v ) 8v48v4 – 3v 3 + 10v 2 8v 4 – 2v 2 + v – 4 – 3v 3 + 12v 2 – 8v – 7v 3. Subtract 3v 3 – 12v 2 + 8v from 8v 4 – 2v 2 + v – 4 – 4

6. For #4-13, find the product. 4. -2x(3x 2 – 5x + 7) –6x 3 + 10x 2 – 14x

7. For #4-13, find the product. 5. (2x + 5)(3x – 4) 6x26x2 – 8x+ 15x– 20 6x 2 + 7x – 20

8. For #4-13, find the product. 6. (5x 2 – 4)(2x 2 + x – 3) 10x 4 + 5x 3 – 15x 2 – 8x 2 10x 4 + 5x 3 – 23x 2 – 4x + 12 – 4x+ 12

9. For #4-13, find the product. 7. (x 2 + 4x + 3)(3x 2 – 7x + 6) 3x43x4 – 7x 3 + 6x 2

10. For #4-13, find the product. 7. (x 2 + 4x + 3)(3x 2 – 7x + 6) 3x43x4 – 7x 3 + 6x 2 + 12x 3 – 28x 2 + 24x

11. For #4-13, find the product. 7. (x 2 + 4x + 3)(3x 2 – 7x + 6) 3x43x4 – 7x 3 + 6x 2 + 12x 3 – 28x 2 + 24x + 9x 2 – 21x+ 18 3x43x4 + 5x 3 – 13x 2 + 3x+ 18

12. For #4-13, find the product. 8. (x + 4)(x – 6)(x – 5) (x2(x2 – 6x+ 4x– 24)(x – 5)

13. For #4-13, find the product. 8. (x + 4)(x – 6)(x – 5) (x2(x2 – 6x+ 4x– 24) (x 2 – 2x – 24)(x – 5) (x – 5) x3x3 – 5x 2

14. For #4-13, find the product. 8. (x + 4)(x – 6)(x – 5) (x2(x2 – 6x+ 4x– 24) (x 2 – 2x – 24)(x – 5) (x – 5) x3x3 – 5x 2 – 2x 2 + 10x

15. For #4-13, find the product. 8. (x + 4)(x – 6)(x – 5) (x2(x2 – 6x+ 4x– 24) (x 2 – 2x – 24)(x – 5) (x – 5) x3x3 – 5x 2 – 2x 2 + 10x– 24x+ 120 x3x3 – 7x 2 – 14x+ 120

16. For #4-13, find the product. 9. (3x + 2)(3x – 2) 9x29x2 – 6x+ 6x– 4 9x29x2 Difference of Squares Pattern: (a + b)(a – b) a 2 – b 2

17. For #4-13, find the product. 10. (2x + 5) 2 Square of a Binomial (positive): (a + b) 2 a 2 + 2ab + b 2 4x24x2 + 10x + 25 4x24x2 + 20x (2x + 5)(2x + 5) + 25

18. For #4-13, find the product. 11. (4x – 7) 2 Square of a Binomial (negative): (a – b) 2 a 2 – 2ab + b 2 16x 2 – 28x + 49 16x 2 – 56x (4x – 7)(4x – 7) + 49

19. For #4-13, find the product. 12. (x + 5) 3 Cube of a Binomial (positive): (a + b) 3 a 3 + 3a 2 b + 3ab 2 + b 3 (x + 5)(x + 5)(x + 5) x3x3 + 5x 2 + 10x 2 + 50x+ 25x+ 125 x3x3 + 15x 2 + 75x+ 125 (x 2 + 10x + 25)(x + 5)

20. For #4-13, find the product. 13. (x – 2) 3 Cube of a Binomial (negative): (a – b) 3 a 3 – 3a 2 b + 3ab 2 – b 3 (x – 2)(x – 2)(x – 2) x3x3 – 2x 2 – 4x 2 – 8x+ 4x– 8 x3x3 – 6x 2 – 4x– 8 (x 2 – 4x + 4)(x – 2)