Basic Math Examples

$4 y^{6} + 256 y^{3}$

Step 1

Factor $4 y^{3}$ out of $4 y^{6} + 256 y^{3}$ .

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Step 1.1

Factor $4 y^{3}$ out of $4 y^{6}$ .

$4 y^{3} (y^{3}) + 256 y^{3}$

Step 1.2

Factor $4 y^{3}$ out of $256 y^{3}$ .

$4 y^{3} (y^{3}) + 4 y^{3} (64)$

Step 1.3

Factor $4 y^{3}$ out of $4 y^{3} (y^{3}) + 4 y^{3} (64)$ .

$4 y^{3} (y^{3} + 64)$

Step 2

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

$4 y^{3} (y^{3} + 4^{3})$

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 $a = y$ and $b = 4$ .

$4 y^{3} ((y + 4) (y^{2} - y \cdot 4 + 4^{2}))$

Step 4

Factor.

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Step 4.1

Simplify.

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Step 4.1.1

Multiply $4$ by $- 1$ .

$4 y^{3} ((y + 4) (y^{2} - 4 y + 4^{2}))$

Step 4.1.2

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

$4 y^{3} ((y + 4) (y^{2} - 4 y + 16))$

Step 4.2

Remove unnecessary parentheses.

$4 y^{3} (y + 4) (y^{2} - 4 y + 16)$