Basic Math Examples

$v^{4} - w^{4}$

Step 1

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

${(v^{2})}^{2} - w^{4}$

Step 2

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

${(v^{2})}^{2} - {(w^{2})}^{2}$

Step 3

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

$(v^{2} + w^{2}) (v^{2} - w^{2})$

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 $a = v$ and $b = w$ .

$(v^{2} + w^{2}) ((v + w) (v - w))$

Step 4.2

Remove unnecessary parentheses.

$(v^{2} + w^{2}) (v + w) (v - w)$