Algebra Examples

a^{4} - b^{4}

$a^{4} - b^{4}$

Step 1

Rewrite

a^{4}

$a^{4}$ as

{(a^{2})}^{2}

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

{(a^{2})}^{2} - b^{4}

${(a^{2})}^{2} - b^{4}$

Step 2

Rewrite

b^{4}

$b^{4}$ as

{(b^{2})}^{2}

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

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

${(a^{2})}^{2} - {(b^{2})}^{2}$

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 = a^{2}

$a = a^{2}$ and

b = b^{2}

$b = b^{2}$ .

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

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

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 = a

$a = a$ and

b = b

$b = b$ .

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

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

Step 4.2

Remove unnecessary parentheses.

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

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

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

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

a^{4} - b^{4}

$a^{4} - b^{4}$

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