Solve left(1+xright)^2+x^2

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

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+x\right)^{2}.

$$1+2x+x^{2}+x^{2}$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$1+2x+2x^{2}$$

Expand

$$2x^{2}+2x+1$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+x\right)^{2}.

$$1+2x+x^{2}+x^{2}$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$1+2x+2x^{2}$$