Sum or Difference of two Cubes
Perfect Cube + or – Perfect Cube
A perfect cube is a number or polynomial that is an exact
third power.
Example:
1, 8, 27, 64, …are perfect cubes since 1 = 1 3,
8 = 2 3, 27 = 3 3 , and 64 = 4 3
…
Factoring the sum or difference of two cubes requires the use
of a special factorization pattern that you need to memorize.
That is:
X 3+ Y 3 = (x + y)(X 2 - XY +
Y 2 )
X 3 -Y 3 = (X - Y)(X 2 + XY +
Y 2 )
The word “SOFAS” is a mnemonic device to help you
memorize this pattern.
Factoring the sum or difference of 2 cubes yields 2 factors.
One is a binomial factor ( 2 terms) and one is a trinomial factor
(3 terms).
TO FACTOR
1. Write the binomial factor.
2 Work from the binomial factor to find the trinomial factor.
(After you find the binomial factor, you may use SOFAS to help
with the trinomial factor.)
Example:
Factor X 3 +125 First, find the binomial factor.
ASK!
| • What term to the third power
equals X 3 ? |
 |
first term |
| • What is the given sign? |
 |
sign |
| • What number to the third power
equals 125? |
 |
second term |
Therefore, the binomial factor is (X + 5). Keep the binomial
factor and use SOFAS to build the trinomial power.
|