FACTORING
BINOMIALS
Factoring Binomials
(4 Possibilities)
• GCF (Greatest Common Factor)
• Difference of Squares
•Sum or Difference of Cubes
• Prime (Not Factorable)
If a GCF exists, simply factor it
out.
10y 12y 2y(5y 6)
5 4
3x 18x 3x(x 6)
2
5x 20x 5x (1 4x )
2 5 2 3
2nd Possibility
DIFFERENCE OF 2
SQUARES
If both terms in the binomial are
squares and they are subtracted, a
Simple Formula will give you the
answer.
a 2
b a ba b
2
Example 1) x 25 ?
2
The Difference of Squares Formula is
a b (a b)(a b)
2 2
Find a and b, then plug them into the formula.
a x2 x
b 25 5
x 25 (x 5)(x 5)
2
Examples of Diff. Of Squares
A B
2 2
(A B)(A B)
x 25 (x 5)(x 5)
2
x 4 (x 2)(x 2)
4 2 2
9x y (3x y)(3x y)
2 2
y 49 (y 7)(y 7)
2
Recognizing Monomial
Squares
Numbers that are perfect squares are: 1, 4, 9, 16, 25, 36…
Variables that are perfect squares are: x 2, y 2, x 4 , x10 , y16
(Any even powered variable is a perfect square)
Monomials that are perfect squares are:
2 2 4
36x ,4y ,25x ,9x ,100y1610
2x2 Check this picture out.
It shows why any even powered
2x2 4x4
Variable is a perfect square.
Try These
x 100 ?
2
x 144 ?
4
16x 4 y ?
2 2
y 1 ?
2
3nd Possibility
SUM or DIFFERENCE OF 2
CUBES
If both binomials are cubes and they
are added
a 3 b 3 a b a 2 ab b 2
If both binomials are cubes and they
are subtracted
a b a b a ab b
3 3
2 2
To solve sum and difference of two cubes, simply solve
for a and b. Then plug into the correct formula.
a 3 b 3 a b a 2 ab b 2
a 3 b3 a b a 2
ab b 2
1. Factor completely 27 x 3 125
27 x 3 125 3x 3 53 3x 5(3x) 2 (3x)(5) (5) 2
a b
a = 3x 3 x 5(9 x 2 15 x 25
b=5
2. Factor completely 7 x 4 448x
7 x x 3 64 GCF FIRST!
a=x
7 xx 4 x 2 4 x 16 b=4
4th and last possibility when trying
to factor a binomial
If the binomial does not have a GCF & is
not a Diff. Of Squares , Diff. of Cubes, or
Sum of Cubes
PRIME & NOT FACTORABLE
Examples of Prime Binomials
x 2
2
4 y 25
2
4x y
2 3
Which binomials are Prime?
4x y
2 10
33x 9
2
121x 100
2
49x y
2