# How to Factor Mathematical Expressions

You often need to *factor* expressions (break those expressions into their simpler components, or *factors*) for calculus. Factoring means “unmultiplying,” like rewriting 12 as

You don’t run across problems like that in calculus, however. For calculus, you need to be able to factor algebraic expressions, like factoring 5*xy** *+ 10*yz* as 5*y*(*x* + 2*z*). Algebraic factoring always involves rewriting a sum or difference of terms as a *product*.

The first step in factoring any type of expression is to pull out — in other words, factor out — the greatest thing that all of the terms have in common — that’s the *greatest common factor**,** *or GCF.

Make sure you always look for a GCF to pull out before trying other factoring techniques.

After you pull out the GCF (if there is one), the next thing to do depends on whether you’re trying to factor a *binomial* (that’s a polynomial with two terms) or a *trinomial* (a three-term polynomial).

If you’re working on a binomial, you should look for one of the following three patterns. The first pattern is *huge*, the next two are much less important.

**Difference of squares:**Knowing how to factor the*di**fference of squares*is critical:Keep in mind that a difference of squares

*can*be factored, but a sum of squares*cannot*be factored. In other words,is prime — you can’t break it up.

**Sum and difference of cubes.**You might also want to memorize the factor rules for the*sum*and*difference*of cubes:and