Algebra Examples

$2 x^{3} - 200 x$

Step 1

Factor out the GCF of $2 x$ from $2 x^{3} - 200 x$ .

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Step 1.1

Factor out the GCF of $2 x$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $2 x$ from the expression $2 x^{3}$ .

$2 x (x^{2}) - 200 x$

Step 1.1.2

Factor out the GCF of $2 x$ from the expression $- 200 x$ .

$2 x (x^{2}) + 2 x (- 100)$

Step 1.2

Since all the terms share a common factor of $2 x$ , it can be factored out of each term.

$2 x (x^{2} - 100)$

Step 2

Rewrite $100$ as $10^{2}$ .

$2 x (x^{2} - 10^{2})$

Step 3

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 $b = 10$ .

$2 x ((x + 10) (x - 10))$