Finite Math Examples

$64 x^{3} + 8 y^{3}$

Step 1

Factor $8$ out of $64 x^{3} + 8 y^{3}$ .

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Step 1.1

Factor $8$ out of $64 x^{3}$ .

$8 (8 x^{3}) + 8 y^{3}$

Step 1.2

Factor $8$ out of $8 y^{3}$ .

$8 (8 x^{3}) + 8 (y^{3})$

Step 1.3

Factor $8$ out of $8 (8 x^{3}) + 8 (y^{3})$ .

$8 (8 x^{3} + y^{3})$

Step 2

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

$8 ({(2 x)}^{3} + y^{3})$

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 $a = 2 x$ and $b = y$ .

$8 ((2 x + y) ({(2 x)}^{2} - (2 x) y + y^{2}))$

Step 4

Factor.

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Step 4.1

Simplify.

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Step 4.1.1

Apply the product rule to $2 x$ .

$8 ((2 x + y) (2^{2} x^{2} - (2 x) y + y^{2}))$

Step 4.1.2

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

$8 ((2 x + y) (4 x^{2} - (2 x) y + y^{2}))$

Step 4.1.3

Multiply $2$ by $- 1$ .

$8 ((2 x + y) (4 x^{2} - 2 x y + y^{2}))$

Step 4.2

Remove unnecessary parentheses.

$8 (2 x + y) (4 x^{2} - 2 x y + y^{2})$