Pre-Algebra Examples

$5 x^{4} - 5 x^{2} + 30 x^{3} y - 30 x y$

Step 1

Factor $5 x$ out of $5 x^{4} - 5 x^{2} + 30 x^{3} y - 30 x y$ .

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Step 1.1

Factor $5 x$ out of $5 x^{4}$ .

$5 x (x^{3}) - 5 x^{2} + 30 x^{3} y - 30 x y$

Step 1.2

Factor $5 x$ out of $- 5 x^{2}$ .

$5 x (x^{3}) + 5 x (- x) + 30 x^{3} y - 30 x y$

Step 1.3

Factor $5 x$ out of $30 x^{3} y$ .

$5 x (x^{3}) + 5 x (- x) + 5 x (6 x^{2} y) - 30 x y$

Step 1.4

Factor $5 x$ out of $- 30 x y$ .

$5 x (x^{3}) + 5 x (- x) + 5 x (6 x^{2} y) + 5 x (- 6 y)$

Step 1.5

Factor $5 x$ out of $5 x (x^{3}) + 5 x (- x)$ .

$5 x (x^{3} - x) + 5 x (6 x^{2} y) + 5 x (- 6 y)$

Step 1.6

Factor $5 x$ out of $5 x (x^{3} - x) + 5 x (6 x^{2} y)$ .

$5 x (x^{3} - x + 6 x^{2} y) + 5 x (- 6 y)$

Step 1.7

Factor $5 x$ out of $5 x (x^{3} - x + 6 x^{2} y) + 5 x (- 6 y)$ .

$5 x (x^{3} - x + 6 x^{2} y - 6 y)$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$5 x ((x^{3} - x) + 6 x^{2} y - 6 y)$

Step 2.2

Factor out the greatest common factor (GCF) from each group.

$5 x (x (x^{2} - 1) + 6 y (x^{2} - 1))$

Step 3

Factor the polynomial by factoring out the greatest common factor, $x^{2} - 1$ .

$5 x ((x^{2} - 1) (x + 6 y))$

Step 4

Rewrite $1$ as $1^{2}$ .

$5 x ((x^{2} - 1^{2}) (x + 6 y))$

Step 5

Factor.

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Step 5.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$5 x ((x + 1) (x - 1) (x + 6 y))$

Step 5.2

Remove unnecessary parentheses.

$5 x (x + 1) (x - 1) (x + 6 y)$