Factor a^5b-64ab

$a^{5} b - 64 a b$

Step 1

Factor $a b$ out of $a^{5} b - 64 a b$ .

Factor $a b$ out of $a^{5} b$ .

$a b (a^{4}) - 64 a b$

Factor $a b$ out of $- 64 a b$ .

$a b (a^{4}) + a b (- 64)$

Factor $a b$ out of $a b (a^{4}) + a b (- 64)$ .

$a b (a^{4} - 64)$

Step 2

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

$a b ({(a^{2})}^{2} - 64)$

Step 3

Rewrite $64$ as $8^{2}$ .

$a b ({(a^{2})}^{2} - 8^{2})$

Step 4

Factor.

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 $b = 8$ .

$a b ((a^{2} + 8) (a^{2} - 8))$

Remove unnecessary parentheses.

$a b (a^{2} + 8) (a^{2} - 8)$

Factor a^5b-64ab

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