Pre-Algebra Examples

$a^{3} b^{3} + 125$

Step 1

Rewrite $a^{3} b^{3}$ as ${(a b)}^{3}$ .

${(a b)}^{3} + 125$

Step 2

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

${(a b)}^{3} + 5^{3}$

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 $a = a b$ and $b = 5$ .

$(a b + 5) ({(a b)}^{2} - (a b) \cdot 5 + 5^{2})$

Step 4

Simplify.

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Step 4.1

Apply the product rule to $a b$ .

$(a b + 5) (a^{2} b^{2} - (a b) \cdot 5 + 5^{2})$

Step 4.2

Remove parentheses.

$(a b + 5) (a^{2} b^{2} - a b \cdot 5 + 5^{2})$

Step 4.3

Multiply $5$ by $- 1$ .

$(a b + 5) (a^{2} b^{2} - 5 a b + 5^{2})$

Step 4.4

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

$(a b + 5) (a^{2} b^{2} - 5 a b + 25)$