Basic Math Examples

$125 + 8 q^{3}$

Step 1

Rewrite $125$ as $5^{3}$ .

$5^{3} + 8 q^{3}$

Step 2

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

$5^{3} + {(2 q)}^{3}$

Step 3

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 $a = 5$ and $b = 2 q$ .

$(5 + 2 q) (5^{2} - 5 (2 q) + {(2 q)}^{2})$

Step 4

Simplify.

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Step 4.1

Raise $5$ to the power of $2$ .

$(5 + 2 q) (25 - 5 (2 q) + {(2 q)}^{2})$

Step 4.2

Multiply $2$ by $- 5$ .

$(5 + 2 q) (25 - 10 q + {(2 q)}^{2})$

Step 4.3

Apply the product rule to $2 q$ .

$(5 + 2 q) (25 - 10 q + 2^{2} q^{2})$

Step 4.4

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

$(5 + 2 q) (25 - 10 q + 4 q^{2})$