Basic Math Examples

$125 z^{3} + 64$

Step 1

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

${(5 z)}^{3} + 64$

Step 2

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

${(5 z)}^{3} + 4^{3}$

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

$(5 z + 4) ({(5 z)}^{2} - (5 z) \cdot 4 + 4^{2})$

Step 4

Simplify.

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Step 4.1

Apply the product rule to $5 z$ .

$(5 z + 4) (5^{2} z^{2} - (5 z) \cdot 4 + 4^{2})$

Step 4.2

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

$(5 z + 4) (25 z^{2} - (5 z) \cdot 4 + 4^{2})$

Step 4.3

Multiply $5$ by $- 1$ .

$(5 z + 4) (25 z^{2} - 5 z \cdot 4 + 4^{2})$

Step 4.4

Multiply $4$ by $- 5$ .

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

Step 4.5

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

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