If a binomial expression can be factored at all, it must be factored in one of four ways. To decide which way you will use, you first look at the addition or subtraction sign that always separates the two terms within the binomial. Then you look at the two terms. Are they squares? Are they cubes? Are they nothing special at all?
The nice thing about having two terms in an expression is that you have only four ways to check:
Finding the greatest common factor (GCF)
Factoring the difference of two perfect squares
Factoring the difference of two perfect cubes
Factoring the sum of two perfect cubes
When you have a factoring problem with two terms, you can go through the list to see which way works. Sometimes the two terms can be factored in more than one way, such as finding the GCF and the difference of two squares.
After you go through one factoring method, check inside the parentheses to see if another factoring can be done. If you checked each item on the list of ways to factor and none works, then you know that the expression can’t be factored any further. You can stop looking and say you’re done.
