Algebra Examples

$a^{3} (x - 2 y) - a x^{2} (x - 2 y)$

Step 1

Factor $a (x - 2 y)$ out of $a^{3} (x - 2 y) - a x^{2} (x - 2 y)$ .

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Step 1.1

Factor $a (x - 2 y)$ out of $a^{3} (x - 2 y)$ .

$a (x - 2 y) (a^{2}) - a x^{2} (x - 2 y)$

Step 1.2

Factor $a (x - 2 y)$ out of $- a x^{2} (x - 2 y)$ .

$a (x - 2 y) (a^{2}) + a (x - 2 y) (- 1 x^{2})$

Step 1.3

Factor $a (x - 2 y)$ out of $a (x - 2 y) (a^{2}) + a (x - 2 y) (- 1 x^{2})$ .

$a (x - 2 y) (a^{2} - 1 x^{2})$

Step 2

Factor.

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Step 2.1

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

$a (x - 2 y) ((a + x) (a - x))$

Step 2.2

Remove unnecessary parentheses.

$a (x - 2 y) (a + x) (a - x)$