Algebra Examples

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

Step 1

Factor $y^{2}$ out of $x^{3} y^{2} - x^{2} y^{3} - x y^{2} + y^{3}$ .

Tap for more steps...

Step 1.1

Factor $y^{2}$ out of $x^{3} y^{2}$ .

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

Step 1.2

Factor $y^{2}$ out of $- x^{2} y^{3}$ .

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

Step 1.3

Factor $y^{2}$ out of $- x y^{2}$ .

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

Step 1.4

Factor $y^{2}$ out of $y^{3}$ .

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

Step 1.5

Factor $y^{2}$ out of $y^{2} x^{3} + y^{2} (- x^{2} y)$ .

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

Step 1.6

Factor $y^{2}$ out of $y^{2} (x^{3} - x^{2} y) + y^{2} (- x)$ .

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

Step 1.7

Factor $y^{2}$ out of $y^{2} (x^{3} - x^{2} y - x) + y^{2} y$ .

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

Step 2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 2.1

Group the first two terms and the last two terms.

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

Step 2.2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Rewrite $1$ as $1^{2}$ .

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

Step 6

Factor.

Tap for more steps...

Step 6.1

Factor.

Tap for more steps...

Step 6.1.1

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 $b = 1$ .

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

Step 6.1.2

Remove unnecessary parentheses.

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

Step 6.2

Remove unnecessary parentheses.

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