Solve (a+b)^2+2(a+b)+1=

$$( a + b ) ^ { 2 } + 2 ( a + b ) + 1 =$$

Evaluate

$$\left(a+b+1\right)^{2}$$

Solution Steps

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

$$a^{2}+2ab+b^{2}+2\left(a+b\right)+1$$

Use the distributive property to multiply 2 by a+b.

$$a^{2}+2ab+b^{2}+2a+2b+1$$

Expand

$$a^{2}+2ab+2a+b^{2}+2b+1$$

Solution Steps

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

$$a^{2}+2ab+b^{2}+2\left(a+b\right)+1$$

Use the distributive property to multiply 2 by a+b.

$$a^{2}+2ab+b^{2}+2a+2b+1$$