8.7 Multiplying Polynomials p.

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

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

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

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

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

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

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

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

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

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

8.8 Special Products p.

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.

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:

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

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

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

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