Algebra Examples

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

Step 1

Regroup terms.

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

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.

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

Step 2.2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Factor $- 1$ out of $- y + x$ .

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Step 5.1

Reorder $- y$ and $x$ .

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

Step 5.2

Factor $- 1$ out of $x$ .

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

Step 5.3

Factor $- 1$ out of $- y$ .

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

Step 5.4

Factor $- 1$ out of $- 1 (- x) - (y)$ .

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

Step 5.5

Rewrite $- 1 (- x + y)$ as $- (- x + y)$ .

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

Step 6

Factor.

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Step 6.1

Factor $- 1$ out of $- x + y$ .

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Step 6.1.1

Factor $- 1$ out of $- x$ .

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

Step 6.1.2

Factor $- 1$ out of $y$ .

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

Step 6.1.3

Factor $- 1$ out of $- (x) - 1 (- y)$ .

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

Step 6.2

Remove unnecessary parentheses.

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

Step 7

Combine exponents.

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Step 7.1

Factor out negative.

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

Step 7.2

Multiply $- 1$ by $- 1$ .

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

Step 7.3

Multiply $x - y$ by $1$ .

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