Factor 7x^4-7

$7 x^{4} - 7$

Step 1

Factor $7$ out of $7 x^{4} - 7$ .

Factor $7$ out of $7 x^{4}$ .

$7 (x^{4}) - 7$

Factor $7$ out of $- 7$ .

$7 (x^{4}) + 7 (- 1)$

Factor $7$ out of $7 (x^{4}) + 7 (- 1)$ .

$7 (x^{4} - 1)$

Step 2

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

$7 ({(x^{2})}^{2} - 1)$

Step 3

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

$7 ({(x^{2})}^{2} - 1^{2})$

Step 4

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 $b = 1$ .

$7 ((x^{2} + 1) (x^{2} - 1))$

Step 5

Factor.

Simplify.

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

$7 ((x^{2} + 1) (x^{2} - 1^{2}))$

Factor.

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 $b = 1$ .

$7 ((x^{2} + 1) ((x + 1) (x - 1)))$

Remove unnecessary parentheses.

$7 ((x^{2} + 1) (x + 1) (x - 1))$

Remove unnecessary parentheses.

$7 (x^{2} + 1) (x + 1) (x - 1)$

Factor 7x^4-7

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