Basic Math Examples

$y^{3} - 4 y$

Step 1

Factor $y$ out of $y^{3} - 4 y$ .

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Step 1.1

Factor $y$ out of $y^{3}$ .

$y \cdot y^{2} - 4 y$

Step 1.2

Factor $y$ out of $- 4 y$ .

$y \cdot y^{2} + y \cdot - 4$

Step 1.3

Factor $y$ out of $y \cdot y^{2} + y \cdot - 4$ .

$y (y^{2} - 4)$

Step 2

Rewrite $4$ as $2^{2}$ .

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

Step 3

Factor.

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Step 3.1

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

$y ((y + 2) (y - 2))$

Step 3.2

Remove unnecessary parentheses.

$y (y + 2) (y - 2)$