Algebra Examples

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

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.

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

Step 1.2

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

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

Step 2

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

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

Step 3

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

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

Step 4

Factor.

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Step 4.1

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 $b = y$ .

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

Step 4.2

Remove unnecessary parentheses.

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

Step 5

Combine exponents.

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Step 5.1

Raise $x - y$ to the power of $1$ .

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

Step 5.2

Raise $x - y$ to the power of $1$ .

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

Step 5.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 5.4

Add $1$ and $1$ .

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