Algebra Examples

x^{4} - y^{4}

$x^{4} - y^{4}$

Step 1

Rewrite

x^{4}

$x^{4}$ as

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

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

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

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

Step 2

Rewrite

y^{4}

$y^{4}$ as

{(y^{2})}^{2}

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

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

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

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 = x^{2}

$a = x^{2}$ and

b = y^{2}

$b = y^{2}$ .

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

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

Step 4

Factor.

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Step 4.1

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 = y

$b = y$ .

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

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

Step 4.2

Remove unnecessary parentheses.

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

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

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

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