Factor v^4-2401

$v^{4} - 2401$

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

${(v^{2})}^{2} - 2401$

Rewrite $2401$ as $49^{2}$ .

${(v^{2})}^{2} - 49^{2}$

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 $b = 49$ .

$(v^{2} + 49) (v^{2} - 49)$

Simplify.

Rewrite $49$ as $7^{2}$ .

$(v^{2} + 49) (v^{2} - 7^{2})$

Factor.

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 $b = 7$ .

$(v^{2} + 49) ((v + 7) (v - 7))$

Remove unnecessary parentheses.

$(v^{2} + 49) (v + 7) (v - 7)$

Factor v^4-2401

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