1. 8.7 Multiplying Polynomials p.

2. The FOIL method is ONLY used when you multiply 2 binomials. F irst terms O utside terms I nside terms L ast terms

3. (y + 3)(y + 7). F tells you to multiply the FIRST terms of each binomial. y2y2

4. (y + 3)(y + 7). O tells you to multiply the OUTSIDE terms of each binomial. y 2 + 7y

5. (y + 3)(y + 7). I tells you to multiply the INSIDE terms of each binomial. y 2 + 7y + 3y

6. (y + 3)(y + 7). L tells you to multiply the LAST terms of each binomial. y 2 + 7y + 3y + 21 Combine like terms. y 2 + 10y + 21

7. Another method is the Box Method. This method works for every problem! Multiply (3x – 5)(5x + 2) Draw a box. Write a polynomial on the top and side of a box. (It does not matter which goes where.) Multiply! 3x-5 5x +2

8. Multiply (2a – 3b)(2a + 4b) *Use the method you prefer. 1.4a 2 + 14ab – 12b 2 2.4a 2 – 14ab – 12b 2 3.4a 2 + 2ab – 12b 2 4.4a 2 – 2ab – 12b 2

9. Multiply (2x - 5)(x 2 - 5x + 4) **You cannot use FOIL because they are not BOTH binomials. You can use the Distributive Property.

10. x2x2 -5x+4 2x -5 Multiply (2x - 5)(x 2 - 5x + 4) Or you can use the Box Method. *Combine Like Terms:

11. Multiply (2p + 1)(p 2 – 3p + 4) 1.2p 3 + 2p 3 + p + 4 2.y 2 – y – 12 3.y 2 + 7y – 12 4.y 2 – 7y – 12

12. 8.8 Special Products p.

13. There are formulas (shortcuts) that work for certain polynomial multiplication problems. (a + b) 2 = a 2 + 2ab + b 2 (a - b) 2 = a 2 – 2ab + b 2 (a - b)(a + b) = a 2 - b 2 Being able to use these formulas will help you in the future when you have to factor. If you do not remember the formulas, you can always use FOIL.

14. Multiply: (x + 4) 2 Use FOIL first then try using (a + b) 2 = a 2 + 2ab + b 2 Shortcut: a is 1 st term, b is the 2 nd term so… a = (x) and b = (4) Plug into the formula a 2 + 2ab + b 2 FOIL:

15. Multiply: (3x + 2y) 2 using (a + b) 2 = a 2 + 2ab + b 2 (3x + 2y) 2 a = (3x) and b = (2y) Plug into the formula: a 2 + 2ab + b 2

16. Multiply: (x – 5) 2 using (a – b) 2 = a 2 – 2ab + b 2 Everything is the same except the signs! You try it! Multiply: (4x – y) 2

17. Multiply (x – 3)(x + 3) using (a – b)(a + b) = a 2 – b 2 You can only use this rule when the binomials are exactly the same except for the sign. (x – 3)(x + 3) a = x and b = 3

18. Multiply: (y – 2)(y + 2) Multiply: (5a + 6b)(5a – 6b)