\(\left(x-1\right)^2+\left(x+1\right)^2\\ =x^2-2x+1+x^2+2x+1\\ =x^2+x^2-2x+2x+1+1\\ =2x^2+2\)
\(\left(x-1\right)^2+\left(x+1\right)^2\)
\(=x^2-2x+1+x^2+2x+1\)
\(=2x^2+2\)
\(=2\left(x^2+1\right)\)
\(\left(x-1\right)^2+\left(x+1\right)^2=\left(x^2-2x+1\right)+\left(x^2+2x+1\right)=x^2-2x+1+x^2+2x+1=2x^2+2\)