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Sum and Difference of Cubes Pattern
The sum and difference of cubes pattern provides specific formulas for factoring binomials composed of two perfect cubes. These cubes factor into the product of a binomial and a trinomial:
Notice that the two formulas share a similar structure but differ in their signs. A helpful way to memorize this pattern is to look at the signs of the factors relative to the original binomial:
- The sign in the binomial factor is identical to the sign in the original expression. A sum of cubes has ; a difference of cubes has .
- The middle term of the trinomial factor always takes the opposite sign of the original expression. A sum of cubes yields ; a difference of cubes yields .
- The first and last terms of the trinomial factor, and , are always positive.
The resulting trinomial factor cannot be factored any further. You can verify the formulas by multiplying the factors using distribution; the middle terms will cancel out, leaving only the original sum or difference of cubes.
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Sum and Difference of Cubes Pattern
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Learn After
How to Factor the Sum or Difference of Cubes
Factoring
Factoring
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