Pre-Algebra Examples

$m^{3} - 343 n^{3}$

Step 1

Rewrite $343 n^{3}$ as ${(7 n)}^{3}$ .

$m^{3} - {(7 n)}^{3}$

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 $a = m$ and $b = 7 n$ .

$(m - (7 n)) (m^{2} + m (7 n) + {(7 n)}^{2})$

Step 3

Simplify.

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Step 3.1

Multiply $7$ by $- 1$ .

$(m - 7 n) (m^{2} + m (7 n) + {(7 n)}^{2})$

Step 3.2

Rewrite using the commutative property of multiplication.

$(m - 7 n) (m^{2} + 7 m n + {(7 n)}^{2})$

Step 3.3

Apply the product rule to $7 n$ .

$(m - 7 n) (m^{2} + 7 m n + 7^{2} n^{2})$

Step 3.4

Raise $7$ to the power of $2$ .

$(m - 7 n) (m^{2} + 7 m n + 49 n^{2})$