Solve (a+b)^2+9(a+b)-10

$$( a + b ) ^ { 2 } + 9 ( a + b ) - 10$$

Evaluate

$$\left(a+b-1\right)\left(a+b+10\right)$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+b\right)^{2}.

$$a^{2}+2ab+b^{2}+9\left(a+b\right)-10$$

Use the distributive property to multiply 9 by a+b.

$$a^{2}+2ab+b^{2}+9a+9b-10$$

Expand

$$a^{2}+2ab+9a+b^{2}+9b-10$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+b\right)^{2}.

$$a^{2}+2ab+b^{2}+9\left(a+b\right)-10$$

Use the distributive property to multiply 9 by a+b.

$$a^{2}+2ab+b^{2}+9a+9b-10$$