Factor 625m^4-81

$625 m^{4} - 81$

Step 1

Rewrite $625 m^{4}$ as ${(25 m^{2})}^{2}$ .

${(25 m^{2})}^{2} - 81$

Step 2

Rewrite $81$ as $9^{2}$ .

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

Step 3

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

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

Step 4

Simplify.

Rewrite $25 m^{2}$ as ${(5 m)}^{2}$ .

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

Rewrite $9$ as $3^{2}$ .

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

Factor.

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

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

Remove unnecessary parentheses.

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

Factor 625m^4-81

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