Factor 1-x^8 - MathMaster

$1 - x^{8}$

Rewrite $1$ as $1^{2}$ .

$1^{2} - x^{8}$

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

$1^{2} - {(x^{4})}^{2}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = x^{4}$ .

$(1 + x^{4}) (1 - x^{4})$

Simplify.

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Rewrite $1$ as $1^{2}$ .

$(1 + x^{4}) (1^{2} - x^{4})$

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

$(1 + x^{4}) (1^{2} - {(x^{2})}^{2})$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = x^{2}$ .

$(1 + x^{4}) ((1 + x^{2}) (1 - x^{2}))$

Factor.

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Simplify.

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Rewrite $1$ as $1^{2}$ .

$(1 + x^{4}) ((1 + x^{2}) (1^{2} - x^{2}))$

Factor.

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Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = x$ .

$(1 + x^{4}) ((1 + x^{2}) ((1 + x) (1 - x)))$

Remove unnecessary parentheses.

$(1 + x^{4}) ((1 + x^{2}) (1 + x) (1 - x))$

Remove unnecessary parentheses.

$(1 + x^{4}) (1 + x^{2}) (1 + x) (1 - x)$

Factor 1-x^8

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