Algebra Examples

x^{4} - 16

$x^{4} - 16$

Step 1

Rewrite

x^{4}

$x^{4}$ as

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

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

{(x^{2})}^{2} - 16

${(x^{2})}^{2} - 16$

Step 2

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

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

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

Step 3

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

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

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

a = x^{2}

$a = x^{2}$ and

b = 4

$b = 4$ .

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

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

Step 4

Simplify.

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Step 4.1

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

Step 4.2

Factor.

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Step 4.2.1

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 = 2

$b = 2$ .

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

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

Step 4.2.2

Remove unnecessary parentheses.

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

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

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

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

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

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

x^{4} - 16

$x^{4} - 16$

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