The Handy Math Answer Book

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Algebra

Polynomial Equations

What is the difference and sum of cubes?

When factoring polynomials, there is the difference and sum of cubes. The difference of cubes takes the form: a3 - b3, and can be factored into (a - b)( a2 + ab + b2). Thus, if an expression resembles a3 - b3, then (a - b) is a factor; use long division to find the remaining factor(s).

The sum of cubes takes the form a3 + b3, and can be factored into (a + b)(a2 + ab + b2). Thus, if an expression resembles a3 + b3, then (a + b) is a factor. Again, use long division to find the remaining factor(s).