Basic Math Examples

$18 a^{2} + 21 a b^{2} + 18 a b + 21 b^{3}$

Step 1

Factor $3$ out of $18 a^{2} + 21 a b^{2} + 18 a b + 21 b^{3}$ .

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Step 1.1

Factor $3$ out of $18 a^{2}$ .

$3 (6 a^{2}) + 21 a b^{2} + 18 a b + 21 b^{3}$

Step 1.2

Factor $3$ out of $21 a b^{2}$ .

$3 (6 a^{2}) + 3 (7 a b^{2}) + 18 a b + 21 b^{3}$

Step 1.3

Factor $3$ out of $18 a b$ .

$3 (6 a^{2}) + 3 (7 a b^{2}) + 3 (6 a b) + 21 b^{3}$

Step 1.4

Factor $3$ out of $21 b^{3}$ .

$3 (6 a^{2}) + 3 (7 a b^{2}) + 3 (6 a b) + 3 (7 b^{3})$

Step 1.5

Factor $3$ out of $3 (6 a^{2}) + 3 (7 a b^{2})$ .

$3 (6 a^{2} + 7 a b^{2}) + 3 (6 a b) + 3 (7 b^{3})$

Step 1.6

Factor $3$ out of $3 (6 a^{2} + 7 a b^{2}) + 3 (6 a b)$ .

$3 (6 a^{2} + 7 a b^{2} + 6 a b) + 3 (7 b^{3})$

Step 1.7

Factor $3$ out of $3 (6 a^{2} + 7 a b^{2} + 6 a b) + 3 (7 b^{3})$ .

$3 (6 a^{2} + 7 a b^{2} + 6 a b + 7 b^{3})$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$3 ((6 a^{2} + 7 a b^{2}) + 6 a b + 7 b^{3})$

Step 2.2

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

$3 (a (6 a + 7 b^{2}) + b (6 a + 7 b^{2}))$

Step 3

Factor.

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Step 3.1

Factor the polynomial by factoring out the greatest common factor, $6 a + 7 b^{2}$ .

$3 ((6 a + 7 b^{2}) (a + b))$

Step 3.2

Remove unnecessary parentheses.

$3 (6 a + 7 b^{2}) (a + b)$