Factor x^2y-9y-3x^2+27

$x^{2} y - 9 y - 3 x^{2} + 27$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{2} y - 9 y) - 3 x^{2} + 27$

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

$y (x^{2} - 9) - 3 (x^{2} - 9)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $x^{2} - 9$ .

$(x^{2} - 9) (y - 3)$

Step 3

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

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

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 $b = 3$ .

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