Factor by Grouping a(x+1)+b(x+1)

$a (x + 1) + b (x + 1)$

Simplify each term.

Apply the distributive property.

$a x + a \cdot 1 + b (x + 1)$

Multiply $a$ by $1$ .

$a x + a + b (x + 1)$

Apply the distributive property.

$a x + a + b x + b \cdot 1$

Multiply $b$ by $1$ .

$a x + a + b x + b$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(a x + a) + b x + b$

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

$a (x + 1) + b (x + 1)$

Factor the polynomial by factoring out the greatest common factor, $x + 1$ .

$(x + 1) (a + b)$