Algebra Examples

$18 x^{3} - 9 x^{2} y - 2 x y^{2} + y^{3}$

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.

$(18 x^{3} - 9 x^{2} y) - 2 x y^{2} + y^{3}$

Step 1.2

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

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

Step 2

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

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

Step 3

Rewrite $- 1 y$ as $- y$ .

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

Step 4

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

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

Step 5

Factor.

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Step 5.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - i^{2} = (a + i) (a - i)$ where $a = 3 x$ and $i = y$ .

$(2 x - y) ((3 x + y) (3 x - y))$

Step 5.2

Remove unnecessary parentheses.

$(2 x - y) (3 x + y) (3 x - y)$