Examples

4 x^{4} - 4

$4 x^{4} - 4$

Step 1

Factor

4

$4$ out of

4 x^{4} - 4

$4 x^{4} - 4$ .

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Step 1.1

Factor

4

$4$ out of

4 x^{4}

$4 x^{4}$ .

4 (x^{4}) - 4

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

Step 1.2

Factor

4

$4$ out of

- 4

$- 4$ .

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

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

Step 1.3

Factor

4

$4$ out of

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

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

4 (x^{4} - 1)

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

4 (x^{4} - 1)

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

Step 2

Rewrite

x^{4}

$x^{4}$ as

{(x^{2})}^{2}

${(x^{2})}^{2}$ .

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

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

Step 3

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

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

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

Step 4

Since both terms are perfect squares, factor using the difference of squares formula,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = x^{2}

$a = x^{2}$ and

b = 1

$b = 1$ .

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

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

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

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

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

Step 5.1.2

Factor.

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Step 5.1.2.1

Since both terms are perfect squares, factor using the difference of squares formula,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = x

$a = x$ and

b = 1

$b = 1$ .

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

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

Step 5.1.2.2

Remove unnecessary parentheses.

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

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

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

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

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

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

Step 5.2

Remove unnecessary parentheses.

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

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

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

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

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