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July 2nd

July 2nd

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.

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1, 8, 27, 64, …are perfect cubes since 1 = 1 3, 8 = 2 3, 27 = 3 3 , and 64 = 4 3

Algebra Buster software can easily solve any algebra problem including sum of cubes such as this one. See how Algebra Buster solves a similar problem

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).

Algebra Buster software will show you all the steps and explanations if you need them. Here are some examples. Our software actually helps you learn Algebra so there is no need to hire an expensive tutor.


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.)


Factor X 3 +125 First, find the binomial factor.


• 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.

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