Algebra Examples

$\frac{m^{2} - n^{2}}{m^{3} + n^{3}}$

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = m$ and $b = n$ .

$\frac{(m + n) (m - n)}{m^{3} + n^{3}}$

Step 2

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

$\frac{(m + n) (m - n)}{(m + n) (m^{2} - m n + n^{2})}$

Step 3

Cancel the common factor of $m + n$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{(m + n) (m - n)}{(m + n) (m^{2} - m n + n^{2})}$

Step 3.2

Rewrite the expression.

$\frac{m - n}{m^{2} - m n + n^{2}}$