Algebra Examples

$3 x^{5} - 75 x^{3}$

Step 1

Factor out the GCF of $3 x^{3}$ from $3 x^{5} - 75 x^{3}$ .

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Step 1.1

Factor out the GCF of $3 x^{3}$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $3 x^{3}$ from the expression $3 x^{5}$ .

$3 x^{3} (x^{2}) - 75 x^{3}$

Step 1.1.2

Factor out the GCF of $3 x^{3}$ from the expression $- 75 x^{3}$ .

$3 x^{3} (x^{2}) + 3 x^{3} (- 25)$

Step 1.2

Since all the terms share a common factor of $3 x^{3}$ , it can be factored out of each term.

$3 x^{3} (x^{2} - 25)$

Step 2

Rewrite $25$ as $5^{2}$ .

$3 x^{3} (x^{2} - 5^{2})$

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 $b = 5$ .

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