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

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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