Basic Math Examples

$y^{5} - 4 y^{7}$

Step 1

Factor $y^{5}$ out of $y^{5} - 4 y^{7}$ .

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Step 1.1

Multiply by $1$ .

$y^{5} \cdot 1 - 4 y^{7}$

Step 1.2

Factor $y^{5}$ out of $- 4 y^{7}$ .

$y^{5} \cdot 1 + y^{5} (- 4 y^{2})$

Step 1.3

Factor $y^{5}$ out of $y^{5} \cdot 1 + y^{5} (- 4 y^{2})$ .

$y^{5} (1 - 4 y^{2})$

Step 2

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

$y^{5} (1^{2} - 4 y^{2})$

Step 3

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

$y^{5} (1^{2} - {(2 y)}^{2})$

Step 4

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 $b = 2 y$ .

$y^{5} ((1 + 2 y) (1 - (2 y)))$

Step 5

Factor.

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Step 5.1

Multiply $2$ by $- 1$ .

$y^{5} ((1 + 2 y) (1 - 2 y))$

Step 5.2

Remove unnecessary parentheses.

$y^{5} (1 + 2 y) (1 - 2 y)$