Factor -x^2y^2+x^4+9y^2-9x^2

$- x^{2} y^{2} + x^{4} + 9 y^{2} - 9 x^{2}$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(- x^{2} y^{2} + x^{4}) + 9 y^{2} - 9 x^{2}$

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

$x^{2} (- 1 y^{2} + x^{2}) - 9 (- y^{2} + x^{2})$

Step 2

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

$(- 1 y^{2} + x^{2}) (x^{2} - 9)$

Step 3

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

$(x^{2} - 1 y^{2}) (x^{2} - 9)$

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 $b = y$ .

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

Step 5

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

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

Step 6

Factor.

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 $b = 3$ .

$(x + y) (x - y) ((x + 3) (x - 3))$

Remove unnecessary parentheses.

$(x + y) (x - y) (x + 3) (x - 3)$