Algebra Examples

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

Step 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 $b = y$ .

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

Step 2

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

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

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $x + y$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $x - y$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

$\frac{x^{2} + x y + y^{2}}{x^{2} + x y + y^{2}}$

Step 3.3

Cancel the common factor of $x^{2} + x y + y^{2}$ .

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Step 3.3.1

Cancel the common factor.

$\frac{x^{2} + x y + y^{2}}{x^{2} + x y + y^{2}}$

Step 3.3.2

Rewrite the expression.

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