8.7 Multiplying Polynomials

p.

The FOIL method is ONLY used when you multiply 2 binomials.

First terms

Outside terms

Inside terms

Last terms

(y + 3)(y + 7). F tells you to multiply the FIRST

terms of each binomial.

y2

(y + 3)(y + 7). O tells you to multiply the OUTSIDE

terms of each binomial.

y2 + 7y

(y + 3)(y + 7). I tells you to multiply the INSIDE

terms of each binomial.

y2 + 7y + 3y

(y + 3)(y + 7). L tells you to multiply the LAST

terms of each binomial.y2 + 7y + 3y + 21

Combine like terms.

y2 + 10y + 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. 4a2 + 14ab – 12b2

2. 4a2 – 14ab – 12b2

3. 4a2 + 2ab – 12b2

4. 4a2 – 2ab – 12b2

Multiply (2x - 5)(x2 - 5x + 4)**You cannot use FOIL because they are not BOTH binomials.

You can use the Distributive Property.

x2 -5x +4

2x

-5

Multiply (2x - 5)(x2 - 5x + 4) Or you can use the Box Method.

*Combine Like Terms:

Multiply (2p + 1)(p2 – 3p + 4)1. 2p3 + 2p3 + p + 4

2. y2 – y – 12

3. y2 + 7y – 12

4. y2 – 7y – 12

8.8 Special Products

p.

There are formulas (shortcuts) that work for certain polynomial multiplication problems.

(a + b)2 = a2 + 2ab + b2

(a - b)2 = a2 – 2ab + b2

(a - b)(a + b) = a2 - b2

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 = a2 + 2ab + b2

Shortcut:a is 1st term, b is the 2nd term

so… a = (x) and b = (4)Plug into the formula

a2 + 2ab + b2

FOIL:

Multiply: (3x + 2y)2

using (a + b)2 = a2 + 2ab + b2

(3x + 2y)2

a = (3x) and b = (2y)

Plug into the formula: a2 + 2ab + b2

Multiply: (x – 5)2

using (a – b)2 = a2 – 2ab + b2

Everything is the same except the signs!

You try it!

Multiply: (4x – y)2

Multiply (x – 3)(x + 3) using (a – b)(a + b) = a2 – b2

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)