Binomial factoring is done two different ways in Algebra 2 depending on the initial binomial. The first step in factoring is to look for a common factor between the two terms. For instance, `2xy^3-10x` has a 2x in common with both terms. Factoring out the GCF (Greatest common factor) looks like:
The factored answer can be checked using distributive property. Here are a couple more examples of factoring out the GCF.
When a GCF does not exist between 2 terms, the binomial either forms a difference of two squares, sum/difference of two cubes, or is prime.
Difference of two squares: `a^2-b^2=(a+b)(a-b)`
Sum of two cubes: `a^3+b^3=(a+b)(a^2-ab+b^2)`
Difference of two cubes: `a^3-b^3=(a-b)(a^2+ab+b^2)`
The 6xy term above came from a=3x and b=2y, so ab=6xy.
For problems like: `9x^2+16y^2`
The answer is prime. No GCF can be found between the two terms and no special relationship exists.