Pre-Algebra Examples

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

Step 1

Factor out the greatest common factor from each group.

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Step 1.1

Group the first two terms and the last two terms.

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

Step 1.2

Factor out the greatest common factor (GCF) from each group.

$x^{2} (- 1 y^{2} + x^{2}) - 4 (- y^{2} + x^{2})$

Step 2

Factor the polynomial by factoring out the greatest common factor, $- 1 y^{2} + x^{2}$ .

$(- 1 y^{2} + x^{2}) (x^{2} - 4)$

Step 3

Reorder $- 1 y^{2}$ and $x^{2}$ .

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

Step 4

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

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

Step 5

Rewrite $4$ as $2^{2}$ .

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

Step 6

Factor.

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Step 6.1

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

$(x + y) (x - y) ((x + 2) (x - 2))$

Step 6.2

Remove unnecessary parentheses.

$(x + y) (x - y) (x + 2) (x - 2)$