Algebra Examples

$x^{8} - y^{8}$

Step 1

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

${(x^{4})}^{2} - y^{8}$

Step 2

Rewrite $y^{8}$ as ${(y^{4})}^{2}$ .

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

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{4}$ and $b = y^{4}$ .

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

Step 4

Simplify.

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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 $b = y^{2}$ .

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

Step 4.4

Factor.

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Step 4.4.1

Factor.

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Step 4.4.1.1

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 $b = y$ .

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

Step 4.4.1.2

Remove unnecessary parentheses.

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

Step 4.4.2

Remove unnecessary parentheses.

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