Algebra Examples

$\frac{x^{3} - y^{3}}{x^{2} - y^{2}}$

Step 1

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 $b = y$ .

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

Step 2

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 $b = y$ .

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

Step 3

Reduce the expression $\frac{(x - y) (x^{2} + x y + y^{2})}{(x + y) (x - y)}$ by cancelling the common factors.

Tap for more steps...

Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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