Calculus Examples

$y - y^{3}$

Step 1

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

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Step 1.1

Raise $y$ to the power of $1$ .

$y^{1} - y^{3}$

Step 1.2

Factor $y$ out of $y^{1}$ .

$y \cdot 1 - y^{3}$

Step 1.3

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

$y \cdot 1 + y (- y^{2})$

Step 1.4

Factor $y$ out of $y \cdot 1 + y (- y^{2})$ .

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

Step 2

Rewrite $1$ as $1^{2}$ .

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

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 $a = 1$ and $b = y$ .

$y ((1 + y) (1 - y))$

Step 3.2

Remove unnecessary parentheses.

$y (1 + y) (1 - y)$