Algebra Examples

16 - x^{4}

$16 - x^{4}$

Step 1

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

4^{2} - x^{4}

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

Step 2

Rewrite

x^{4}

$x^{4}$ as

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

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

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

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

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 = 4

$a = 4$ and

b = x^{2}

$b = x^{2}$ .

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

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

Step 4

Simplify.

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Step 4.1

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

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 = 2

$a = 2$ and

b = x

$b = x$ .

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

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

Step 4.2.2

Remove unnecessary parentheses.

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

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

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

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

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

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

16 - x^{4}

$16 - x^{4}$

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