Online Calculators

# Difference of Two Squares Calculator

Difference of 2 Squares
$a^2 - b^2 = \; ?$

$4(x + 3y^{2})(x - 3y^{2})$
Solution:
Factor the equation$4x^{2} - 36y^{4}$using the identity$a^2 - b^2 = (a + b)(a - b)$First factor out the GCF:$4(x^{2} - 9y^{4})$Both terms are perfect squares so
from a2 - b2 we can find a and b.$a = \sqrt[]{x^{2}} = x$$b = \sqrt[]{9y^{4}} = 3y^{2}$Therefore$a^2 - b^2 = (x)^2 - (3y^{2})^2$Complete the factoring of a2 - b2
to (a + b)(a - b)$4(x + 3y^{2})(x - 3y^{2})$Final Answer:$4(x + 3y^{2})(x - 3y^{2})$

## 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 a2 - b2 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:

$$a^2 - b^2 = (a + b)(a - b)$$

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 -a2 - b2 the equation is not in the form of a2 - b2and cannot be rearranged into this form.

If a is negative and we have addition such that we have -a2 + b2 the equation can be rearranged to the form of b2 - a2which is the correct equation only the letters a and b are switched;  we can just rename our terms.

For example, factor the equation

$$-4y^{2} + 36$$

We can rearrange this equation to

$$36 - 4y^{2}$$

and now solve the difference of two squares with a = 36 and b = 4y2

Solution:

Factor the equation (rearranged)

$$36 - 4y^{2}$$

using the identity

$$a^2 - b^2 = (a + b)(a - b)$$

First factor out the GCF:

$$4(9 - y^{2})$$

Both terms are perfect squares so from a2 - b2 we can find a and b.

$$a = \sqrt[]{9} = 3$$
$$b = \sqrt[]{y^{2}} = y$$

Therefore

$$a^2 - b^2 = (3)^2 - (y)^2$$

Complete the factoring of a2 - b2 to (a + b)(a - b)

$$4(3 + y)(3 - y)$$

$$4(3 + y)(3 - y)$$