Algebra Examples

$r^{3} - 27$

Step 1

Rewrite $27$ as $3^{3}$ .

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

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 $b = 3$ .

$(r - 3) (r^{2} + r \cdot 3 + 3^{2})$

Step 3

Simplify.

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Step 3.1

Move $3$ to the left of $r$ .

$(r - 3) (r^{2} + 3 r + 3^{2})$

Step 3.2

Raise $3$ to the power of $2$ .

$(r - 3) (r^{2} + 3 r + 9)$