Multiply Polynomials

When multiplying polynomials, we always use When multiplying polynomials, we always use the the Distributive PropertyDistributive Property. .

-x(4x2 + x - 8) + 7(4x2 + x - 8).-4x3 – x2 + 8x + 28x2 + 7x - 56

Combine like terms.-4x3 + 27x2 + 15x - 56

x(-4x2 + 5x - 2) - 3(-4x2 + 5x - 2).

-4x3 + 5x2 - 2x + 12x2 - 15x + 6Combine like terms.

-4x3 + 17x2 - 17x + 6

A SHORTCUTSHORTCUT of the distributive property is called the FOIL

method.

6x2

F O I LFirst

F O I LFirst

6x2 - 8x

Outer

F O I LFirst Outer Inner

6x2 - 8x + 3x

Combine like terms.

6x2 - 5x - 4

F O I LFirst

6x2 - 8x + 3x - 4

Outer Inner Last

First terms

Outer terms

Inner terms

Last terms

F O I L

5x(3x) + 5x(-2) + 2(3x) + 2(-2).15x2 – 10x + 6x - 4Combine like terms.

15x2 – 4x - 4

F O I L

2x2 + 7x – 8x – 28Combine like terms.

2x2 – x – 28

F O I L

2x2 – 18x + 3x – 27Combine like terms.

2x2 – 15x – 27

(x + 3) (2x – 7)= 2x2 – 7x + 6x – 21Combine like terms.

2x2 - x - 21

(x + 3)

(2x - 7)(2x-7)

Write a polynomial that represents the area of the shaded region:

(x + 3)

(2x - 7)(x+6)