Factor by Grouping 8a^3+(a+b)^3

$8 a^{3} + {(a + b)}^{3}$

Step 1

Use the Binomial Theorem.

$8 a^{3} + a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}$

Step 2

Add $8 a^{3}$ and $a^{3}$ .

$9 a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}$

Step 3

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(9 a^{3} + 3 a^{2} b) + 3 a b^{2} + b^{3}$

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

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

Step 4

Factor the polynomial by factoring out the greatest common factor, $3 a + b$ .

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