Algebra Examples

$r^{3} - 8$

Step 1

Rewrite $8$ as $2^{3}$ .

$r^{3} - 2^{3}$

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 $a = r$ and $b = 2$ .

$(r - 2) (r^{2} + r \cdot 2 + 2^{2})$

Step 3

Simplify.

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Step 3.1

Move $2$ to the left of $r$ .

$(r - 2) (r^{2} + 2 r + 2^{2})$

Step 3.2

Raise $2$ to the power of $2$ .

$(r - 2) (r^{2} + 2 r + 4)$