Algebra Examples

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

Step 1

Rewrite $a^{4}$ as ${(a^{2})}^{2}$ .

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

Step 2

Rewrite $b^{4}$ as ${(b^{2})}^{2}$ .

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

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a^{2}$ and $b = b^{2}$ .

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

Step 4

Factor.

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Step 4.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = b$ .

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

Step 4.2

Remove unnecessary parentheses.

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