Algebra Examples

$x^{2} y - 9 y + 45 - 5 x^{2}$

Step 1

Regroup terms.

$- 9 y + x^{2} y + 45 - 5 x^{2}$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$(- 9 y + x^{2} y) + 45 - 5 x^{2}$

Step 2.2

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

$y \cdot (- 9 + x^{2}) - 5 (- 9 + x^{2})$

Step 3

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

$(- 9 + x^{2}) (y - 5)$

Step 4

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

$(- 3^{2} + x^{2}) (y - 5)$

Step 5

Reorder $- 3^{2}$ and $x^{2}$ .

$(x^{2} - 3^{2}) (y - 5)$

Step 6

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 $b = 3$ .

$(x + 3) (x - 3) (y - 5)$