Pre-Algebra Examples

$27 m^{3} + n^{3}$

Step 1

Rewrite $27 m^{3}$ as ${(3 m)}^{3}$ .

${(3 m)}^{3} + n^{3}$

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 $a = 3 m$ and $b = n$ .

$(3 m + n) ({(3 m)}^{2} - (3 m) n + n^{2})$

Step 3

Simplify.

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Step 3.1

Apply the product rule to $3 m$ .

$(3 m + n) (3^{2} m^{2} - (3 m) n + n^{2})$

Step 3.2

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

$(3 m + n) (9 m^{2} - (3 m) n + n^{2})$

Step 3.3

Multiply $3$ by $- 1$ .

$(3 m + n) (9 m^{2} - 3 m n + n^{2})$