Algebra Examples

$3 a^{3} - 3 a b^{2} + a^{2} b - b^{3}$

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.

$(3 a^{3} - 3 a b^{2}) + a^{2} b - b^{3}$

Step 1.2

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

$3 a (a^{2} - 1 b^{2}) + b (a^{2} - b^{2})$

Step 2

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

$(a^{2} - 1 b^{2}) (3 a + b)$

Step 3

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

$(a + b) (a - b) (3 a + b)$