Pre-Algebra Examples

$2 y^{4} - 98 x^{2} y^{2}$

Step 1

Factor $2 y^{2}$ out of $2 y^{4} - 98 x^{2} y^{2}$ .

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Step 1.1

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

$2 y^{2} (y^{2}) - 98 x^{2} y^{2}$

Step 1.2

Factor $2 y^{2}$ out of $- 98 x^{2} y^{2}$ .

$2 y^{2} (y^{2}) + 2 y^{2} (- 49 x^{2})$

Step 1.3

Factor $2 y^{2}$ out of $2 y^{2} (y^{2}) + 2 y^{2} (- 49 x^{2})$ .

$2 y^{2} (y^{2} - 49 x^{2})$

Step 2

Rewrite $49 x^{2}$ as ${(7 x)}^{2}$ .

$2 y^{2} (y^{2} - {(7 x)}^{2})$

Step 3

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 $b = 7 x$ .

$2 y^{2} ((y + 7 x) (y - (7 x)))$

Step 4

Factor.

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Step 4.1

Multiply $7$ by $- 1$ .

$2 y^{2} ((y + 7 x) (y - 7 x))$

Step 4.2

Remove unnecessary parentheses.

$2 y^{2} (y + 7 x) (y - 7 x)$