Pre-Algebra Examples

$64 - 125 a^{3}$

Step 1

Rewrite $64$ as $4^{3}$ .

$4^{3} - 125 a^{3}$

Step 2

Rewrite $125 a^{3}$ as ${(5 a)}^{3}$ .

$4^{3} - {(5 a)}^{3}$

Step 3

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 $a = 4$ and $b = 5 a$ .

$(4 - (5 a)) (4^{2} + 4 (5 a) + {(5 a)}^{2})$

Step 4

Simplify.

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Step 4.1

Multiply $5$ by $- 1$ .

$(4 - 5 a) (4^{2} + 4 (5 a) + {(5 a)}^{2})$

Step 4.2

Raise $4$ to the power of $2$ .

$(4 - 5 a) (16 + 4 (5 a) + {(5 a)}^{2})$

Step 4.3

Multiply $5$ by $4$ .

$(4 - 5 a) (16 + 20 a + {(5 a)}^{2})$

Step 4.4

Apply the product rule to $5 a$ .

$(4 - 5 a) (16 + 20 a + 5^{2} a^{2})$

Step 4.5

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

$(4 - 5 a) (16 + 20 a + 25 a^{2})$