Finite Math Examples

$x^{4} y + 8 x y$

Step 1

Factor $x y$ out of $x^{4} y + 8 x y$ .

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Step 1.1

Factor $x y$ out of $x^{4} y$ .

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

Step 1.2

Factor $x y$ out of $8 x y$ .

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

Step 1.3

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

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

Step 2

Rewrite $8$ as $2^{3}$ .

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

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

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

Step 4

Factor.

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Step 4.1

Simplify.

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Step 4.1.1

Multiply $2$ by $- 1$ .

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

Step 4.1.2

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

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

Step 4.2

Remove unnecessary parentheses.

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