Algebra Examples

\frac{a^{3} - b^{3}}{a^{2} - b^{2}}

$\frac{a^{3} - b^{3}}{a^{2} - b^{2}}$

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})

$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where

a = a

$a = a$ and

b = b

$b = b$ .

\frac{(a - b) (a^{2} + a b + b^{2})}{a^{2} - b^{2}}

$\frac{(a - b) (a^{2} + a b + b^{2})}{a^{2} - b^{2}}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = a

$a = a$ and

b = b

$b = b$ .

\frac{(a - b) (a^{2} + a b + b^{2})}{(a + b) (a - b)}

$\frac{(a - b) (a^{2} + a b + b^{2})}{(a + b) (a - b)}$

Step 3

Cancel the common factor of

a - b

$a - b$ .

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Step 3.1

Cancel the common factor.

$\frac{(a - b) (a^{2} + a b + b^{2})}{(a + b) (a - b)}$

Step 3.2

Rewrite the expression.

$\frac{a^{2} + a b + b^{2}}{a + b}$