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

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

Evaluate

$$2a\left(a+b\right)+\left(a+b\right)^{2}+81$$

Solution Steps

Calculate 9 to the power of 2 and get 81.

$$81+2a\left(a+b\right)+\left(a+b\right)^{2}$$

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

$$81+2a^{2}+2ab+\left(a+b\right)^{2}$$

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

$$81+2a^{2}+2ab+a^{2}+2ab+b^{2}$$

Combine 2a^{2} and a^{2} to get 3a^{2}.

$$81+3a^{2}+2ab+2ab+b^{2}$$

Combine 2ab and 2ab to get 4ab.

$$81+3a^{2}+4ab+b^{2}$$

Expand

$$3a^{2}+4ab+b^{2}+81$$

Solution Steps

Calculate 9 to the power of 2 and get 81.

$$81+2a\left(a+b\right)+\left(a+b\right)^{2}$$

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

$$81+2a^{2}+2ab+\left(a+b\right)^{2}$$

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

$$81+2a^{2}+2ab+a^{2}+2ab+b^{2}$$

Combine 2a^{2} and a^{2} to get 3a^{2}.

$$81+3a^{2}+2ab+2ab+b^{2}$$

Combine 2ab and 2ab to get 4ab.

$$81+3a^{2}+4ab+b^{2}$$