Algebra Examples

$x^{4} - y^{4}$

Step 1

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Step 2

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

${(x^{2})}^{2} - {(y^{2})}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{2}$ and $b = y^{2}$ .

$(x^{2} + y^{2}) (x^{2} - y^{2})$

Step 4

Factor.

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Step 4.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = y$ .

$(x^{2} + y^{2}) ((x + y) (x - y))$

Step 4.2

Remove unnecessary parentheses.

$(x^{2} + y^{2}) (x + y) (x - y)$