# Difference of Two Squares Calculator

## Calculator Use

This is a factoring calculator if specifically for the factorization of the difference of two squares. If the input equation can be put in the form of a^{2} - b^{2} it will be factored. The work for the solution will be shown for factoring out any greatest common factors then calculating a difference of 2 squares using the idenity:

Factored terms that contain additional differences of two squares will also be factored.

## Difference of Two Squares when a is Negative

If both terms a and b are negative such that we have -a^{2} - b^{2} the equation is not in the form of a^{2} - b^{2}and cannot be rearranged into this form.

If a is negative and we have addition such that we have -a^{2} + b^{2} the equation can be rearranged to the form of b^{2} - a^{2}which is the correct equation only the letters a and b are switched; we can just rename our terms.

For example, factor the equation

We can rearrange this equation to

and now solve the difference of two squares with a = 36 and b = 4y^{2}

Solution:

Factor the equation (rearranged)

using the identity

First factor out the GCF:

Both terms are perfect squares so from a^{2} - b^{2} we can find a and b.

Therefore

Complete the factoring of a^{2} - b^{2} to (a + b)(a - b)

Final Answer: