Difference of Two Squares Calculator

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Algebra

Difference of 2 Squares

\[ a^2 - b^2 = \; ? \]

Enter an Equation:

Answer:

\[ 4(x + 3y^{2})(x - 3y^{2}) \]

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:\[ 4(x + 3y^{2})(x - 3y^{2}) \]

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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)

\( 4(3 + y)(3 - y) \)

Final Answer:

\( 4(3 + y)(3 - y) \)