Pre-Algebra Examples

$w^{4} y^{2} - 81 y^{2}$

Step 1

Factor $y^{2}$ out of $w^{4} y^{2} - 81 y^{2}$ .

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Step 1.1

Factor $y^{2}$ out of $w^{4} y^{2}$ .

$y^{2} w^{4} - 81 y^{2}$

Step 1.2

Factor $y^{2}$ out of $- 81 y^{2}$ .

$y^{2} w^{4} + y^{2} \cdot - 81$

Step 1.3

Factor $y^{2}$ out of $y^{2} w^{4} + y^{2} \cdot - 81$ .

$y^{2} (w^{4} - 81)$

Step 2

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

$y^{2} ({(w^{2})}^{2} - 81)$

Step 3

Rewrite $81$ as $9^{2}$ .

$y^{2} ({(w^{2})}^{2} - 9^{2})$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = w^{2}$ and $b = 9$ .

$y^{2} ((w^{2} + 9) (w^{2} - 9))$

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

Rewrite $9$ as $3^{2}$ .

$y^{2} ((w^{2} + 9) (w^{2} - 3^{2}))$

Step 5.1.2

Factor.

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Step 5.1.2.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = w$ and $b = 3$ .

$y^{2} ((w^{2} + 9) ((w + 3) (w - 3)))$

Step 5.1.2.2

Remove unnecessary parentheses.

$y^{2} ((w^{2} + 9) (w + 3) (w - 3))$

Step 5.2

Remove unnecessary parentheses.

$y^{2} (w^{2} + 9) (w + 3) (w - 3)$