Calculus Examples

$4 p q^{4} - 4 p r^{4}$

Step 1

Factor out the GCF of $4 p$ from $4 p q^{4} - 4 p r^{4}$ .

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Step 1.1

Factor out the GCF of $4 p$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $4 p$ from the expression $4 p q^{4}$ .

$4 p (q^{4}) - 4 p r^{4}$

Step 1.1.2

Factor out the GCF of $4 p$ from the expression $- 4 p r^{4}$ .

$4 p (q^{4}) + 4 p (- r^{4})$

Step 1.2

Since all the terms share a common factor of $4 p$ , it can be factored out of each term.

$4 p (q^{4} - r^{4})$

Step 2

Rewrite $q^{4}$ as ${(q^{2})}^{2}$ .

$4 p ({(q^{2})}^{2} - r^{4})$

Step 3

Rewrite $r^{4}$ as ${(r^{2})}^{2}$ .

$4 p ({(q^{2})}^{2} - {(r^{2})}^{2})$

Step 4

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

$4 p ((q^{2} + r^{2}) (q^{2} - r^{2}))$

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 $a = q$ and $b = r$ .

$4 p ((q^{2} + r^{2}) ((q + r) (q - r)))$

Step 5.2

Remove unnecessary parentheses.

$4 p ((q^{2} + r^{2}) (q + r) (q - r))$