Multiplying Polynomials

Module VII, Lesson 3

Online Algebra

VHS@PWCS

Multiplying Polynomials

Recall that to multiply a polynomial by a monomial, we used the distributive

property.

3x(2x2 – 7x + 8)

3x(2x2) – 3x(7x) + 3x(8)

6x3 – 21x2 + 24x

Multiplying Binomials

We apply the distributive property when multiplying binomials using a method called FOIL.

FOIL stands for:First – Multiply the first terms

Outside – Multiply the outside terms

Inside – Multiply the inside terms

Last – Multiply the last terms

x( + )( + )5 x 7

x(x)+ 7x + 5x+ 5(7)

x2 +12x + 35

Try these using FOIL

(x – 8)(x + 7)

Firstx(x) = x2

Outside7x

Inside -8x

Last-8(7) = -56

Put it all together:x2 + 7x + -8x + -56

x2 - x - 56

(2x + 9)(3x – 10)

First2x(3x) = 6x2

Outside2x(-10) = -20x

Inside 9(3x) = 27x

Last9(-10) = -56

Put it all together:6x2 + -20x + 27x + -56

6x2 + 7x - 56

Multiplying Polynomials by Polynomials

(3x2 – 2x + 3)(2x + 7)Like with adding and subtracting

polynomials it is easier to multiply setting these on top of each other.

In this manner we can multiply as we have always done.

1. Multiply everything in the first factor by 7

2. Multiply everything in the first factor by 2x, using a placeholder.

3. Add the products.

23 2 3

2 7

x x

x

221 14 21x x 3 26 4 6x x x

6x3 + 17x2 – 8x + 21

Try these on your own.

(x – 3)(2x2 + 3x + 3)

2x2 + 3x + 3

x – 3

-6x2 – 9x – 9

2x3 + 3x2 + 3x

2x3 - 3x2 - 6x - 9

(2t2 – 6t + 3)(2t – 5)

2t2 – 6t + 3

2t – 5

-10t2 + 30t – 15

4t3 – 12t2 + 6t

4t3 – 22t2 + 36t - 15

Wrap up

We use FOIL to multiply 2 binomials First Outside Inside Last

We can set up multiplying polynomials as we have always done and follow those rules.