Factor 3a^3+6a^2b+3a^2+6ab

$3 a^{3} + 6 a^{2} b + 3 a^{2} + 6 a b$

Step 1

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

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

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

Factor $3 a$ out of $6 a^{2} b$ .

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

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

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

Factor $3 a$ out of $6 a b$ .

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

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

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

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

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

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

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$3 a (a (a + 2 b) + 1 (a + 2 b))$

Step 3

Factor.

Factor the polynomial by factoring out the greatest common factor, $a + 2 b$ .

$3 a ((a + 2 b) (a + 1))$

Remove unnecessary parentheses.

$3 a (a + 2 b) (a + 1)$