MTH 100
Factoring Special Polynomials
Overview
• Special polynomials fall into three broad
categories:
1. Difference of Squares
a2 – b2 = (a + b)(a – b)
• Both terms are perfect squares.
• There is a subtraction sign between the terms.
x  121
2
25 x  144
2
2 x  72
2
2. Sum/Difference of Cubes
a3 + b3 = (a + b)(a2 – ab + b2)
a3 – b3 = (a – b)(a2 + ab + b2)
• Both terms are perfect cubes.
• Pay close attention to the factor patterns,
and watch your signs.
• The trinomial in the pattern does not factor
again.
Examples
8b  g
3
3
x  343
3
8m  216n
3
3
3. Perfect Square Trinomials
a2 – 2ab + b2 = (a – b)(a – b) = (a – b)2
a2 + 2ab + b2 = (a + b)(a + b) = (a + b)2
• The first and last terms are perfect squares.
• The last sign is positive.
• The middle term is two times the square root
of the first and last terms.
Examples
x  2x 1
2
49 y  56 y  16
2
y  8 y  16
6
3
4. And if by chance they are not
special…
1. Look for a GCF
2. Count the terms:
a) Two terms? Check for difference of squares
or sum/difference of cubes.
b) Three terms? Check for perfect square
trinomial. If not, guess-and-check or AC.
c) Four terms? Try factor by grouping.
Examples
15b  95b  70
2
24 y  10 y  6 y
3
2 y  54 y
6
2
3