Factor 81m^4-625

$81 m^{4} - 625$

Step 1

Rewrite $81 m^{4}$ as ${(9 m^{2})}^{2}$ .

${(9 m^{2})}^{2} - 625$

Step 2

Rewrite $625$ as $25^{2}$ .

${(9 m^{2})}^{2} - 25^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 9 m^{2}$ and $b = 25$ .

$(9 m^{2} + 25) (9 m^{2} - 25)$

Step 4

Simplify.

Rewrite $9 m^{2}$ as ${(3 m)}^{2}$ .

$(9 m^{2} + 25) ({(3 m)}^{2} - 25)$

Rewrite $25$ as $5^{2}$ .

$(9 m^{2} + 25) ({(3 m)}^{2} - 5^{2})$

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 m$ and $b = 5$ .

$(9 m^{2} + 25) ((3 m + 5) (3 m - 5))$

Remove unnecessary parentheses.

$(9 m^{2} + 25) (3 m + 5) (3 m - 5)$

Factor 81m^4-625

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