Algebra Examples

$9 x^{2} y^{4} - 16 y^{2} z^{6}$

Step 1

Factor $y^{2}$ out of $9 x^{2} y^{4} - 16 y^{2} z^{6}$ .

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Step 1.1

Factor $y^{2}$ out of $9 x^{2} y^{4}$ .

$y^{2} (9 x^{2} y^{2}) - 16 y^{2} z^{6}$

Step 1.2

Factor $y^{2}$ out of $- 16 y^{2} z^{6}$ .

$y^{2} (9 x^{2} y^{2}) + y^{2} (- 16 z^{6})$

Step 1.3

Factor $y^{2}$ out of $y^{2} (9 x^{2} y^{2}) + y^{2} (- 16 z^{6})$ .

$y^{2} (9 x^{2} y^{2} - 16 z^{6})$

Step 2

Rewrite $9 x^{2} y^{2}$ as ${(3 x y)}^{2}$ .

$y^{2} ({(3 x y)}^{2} - 16 z^{6})$

Step 3

Rewrite $16 z^{6}$ as ${(4 z^{3})}^{2}$ .

$y^{2} ({(3 x y)}^{2} - {(4 z^{3})}^{2})$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 x y$ and $b = 4 z^{3}$ .

$y^{2} ((3 x y + 4 z^{3}) (3 x y - (4 z^{3})))$

Step 5

Factor.

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Step 5.1

Multiply $4$ by $- 1$ .

$y^{2} ((3 x y + 4 z^{3}) (3 x y - 4 z^{3}))$

Step 5.2

Remove unnecessary parentheses.

$y^{2} (3 x y + 4 z^{3}) (3 x y - 4 z^{3})$