Factoring GCF and DOPS
Name:
Factor each expression below by finding the greatest common factor (GCF).
4x + 8y
15x2y3 + 10xy2
2x 3 – 6x
15x 3 – 10x
8x + 16xy
4x + 4y
4r - 6r 2
13a 2  26a 3
3x 3  6 x 2  9 xy
A special kind of expression is called the difference of perfect squares (sometimes known as DOPS). This
is factorable in a fun way!
x 2  y 2  ( x  y)( x  y)
Example: x 2  16  ( x  4)( x  4)
Be careful!
DOPS does NOT apply to a 2 + b 2.
It is not the SUM of 2 perfect squares!
a 2 + b 2 is prime i.e. not factorable
Factor each expression below.
x2- 9
x2- 16
x2- 64
Factor each DOPS expression below.
x2 – 81
x2 – 100
x2 – 1
25 – x2
x2 – 144
4x2 – 169
Factoring Completely. Sometimes you need to go through more than one step to completely factor an
expression.
Factor 4y2 - 36y6
1st Factor out a GCF
2nd Now we have DOPS! Factor again. 
Factor completely each expression below.
x3 – 9x
2m2 – 2
64y – y3
3x3 – 12x
3x3  27 x
20m2 – 5
Challenge: Factor completely:
x4  y4