# How to factor a perfect cube

College algebra students learn How to factor a perfect cube, and manipulate different types of functions.

## Factoring Perfect Cubes: Formula & Examples

So, to factor, I'll be plugging 3x and 1 into the sum-of-cubes formula. This gives me: 27 x3 + 1 = (3 x) 3 + 1 3 = (3 x + 1) ( (3 x) 2 − (3 x ) (1) + 1 2) = (3x + 1) (9x2 − 3x + 1) Content Continues Below

## Factoring and Perfect Cubes

!a3 + b3 = (a + b) (a2 - ab + b2) Factor the Difference of Perfect Cubes: a3 - b3 = (a - b) (a2 + ab + b2) When trying to remember these patterns, remember that the first binomial term in the factored form in each pattern keeps the same sign as the sign between the perfect cubes. The sign separating the first and second terms of the trinomial is opposite the sign between the perfect cubes, and the last sign in the trinomial is always positive.

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