multiply polynomials when multiplying polynomials, we always use the distributive property
TRANSCRIPT
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)