Multiplying Binomials
Mentally
The Distributive Property
(x + 5)(2x + 6)
(x+5) 2x + (x+5)6
2x(x+5) +6(x+5)
2x² + 10x + 6x + 30
2x² + 16x +30
NOTE : Since there are THREE terms this
is called a TRINOMIAL
Trinomials
Multiplying MOST binomials results in
THREE terms
You can learn to multiply binomials in
your head by using a method called
FOIL
The FOIL Method
(x + 4)(x +2)
first terms
last terms
(x + 4) ( x + 2)
inner terms
outer terms
(x + 4) ( x + 2)
Now write the products
x² + 2x + 4 x + 8
first
outer inner
last
terms terms terms terms
To Multiply any two binomials
and write the result as a
TRINOMIAL follow these steps
multiply the first two terms
multiply the two outer terms
multiply the two inner terms
multiply the last two terms
Special Cases
There are several special cases of
multiplying binomials
Difference of Squares
Perfect Square Trinomials
Difference of two squares
When you multiply the sum of two
terms and the difference of two terms
you get a BINOMIAL
(a + b) (a – b) = a² - b²
This binomial is the difference of two
squares
A Closer Look
(k – 4) (k + 4)
Using FOIL
k ² + 4k - 4k - 16
k ² - 16
(6c – 3) ( 6c + 3)
Using FOIL
36c² +18c – 18c – 9
Squaring A Binomial
When you square any binomial(that is
multiply it by itself) you get a TRINOMIAL
(x+9)² means (x+9)(x+9)
Using FOIL
x² + 9x + 9x + 81
x² + 18x +81
This is called a PERFECT SQUARE TRINOMIAL
REMEMBER: The square of a
binomial is the sum of three
things:
The square of the first term
Twice the product of the terms
The square of its last term
Perfect Square Trinomials
(3x – 6 )² = (3x - 6) (3x – 6)
9x² – 36 x + 36
(2m –4)² = (2m - 4)( 2m – 4)
4m² –16m + 16
An example
(6x + 3)²
The square of the first term: 36 x²
Twice the product of the terms
2( 6x • 3) +36 x
The square of the last terms
(3)(3) +9
36x² + 36x + 9
Perfect Square Trinomial
patterns
(a + b)²
= a² + 2ab + b²
( a – b)² = a ² - 2ab + b²