Algebra Examples

$p^{4} - p^{3} q + p q^{3} - q^{4}$

Step 1

Factor out the greatest common factor from each group.

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Step 1.1

Group the first two terms and the last two terms.

$(p^{4} - p^{3} q) + p q^{3} - q^{4}$

Step 1.2

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

$p^{3} (p - 1 q) + q^{3} (p - q)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $p - 1 q$ .

$(p - 1 q) (p^{3} + q^{3})$

Step 3

Rewrite $- 1 q$ as $- q$ .

$(p - q) (p^{3} + q^{3})$

Step 4

Factor.

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Step 4.1

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 $a = p$ and $b = q$ .

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

Step 4.2

Remove unnecessary parentheses.

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