Algebra Examples

$m^{3} + 8 n^{3}$

Step 1

Rewrite $8 n^{3}$ as ${(2 n)}^{3}$ .

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

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 $b = 2 n$ .

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

Step 3

Simplify.

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Step 3.1

Rewrite using the commutative property of multiplication.

$(m + 2 n) (m^{2} - 1 \cdot 2 m n + {(2 n)}^{2})$

Step 3.2

Multiply $- 1$ by $2$ .

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

Step 3.3

Apply the product rule to $2 n$ .

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

Step 3.4

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

$(m + 2 n) (m^{2} - 2 m n + 4 n^{2})$