Simplify ((x^2-y^2)(x^2+xy+y^2))/((x^3-y^3)(x+y))

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

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 $b = y$ .

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

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 $b = y$ .

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

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x + y$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - y$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

Cancel the common factor.

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

Rewrite the expression.

$1$

Simplify ((x^2-y^2)(x^2+xy+y^2))/((x^3-y^3)(x+y))

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