Question

(x^2+x+2)^2+(x-1)^2-2(x^2+x+2)(x-1)

Answer 1

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

\(=x^4+x^2+4+2x^3+4x^2+4x+x^2-2x+1-2x^3+2x^2-2x^2+2x-4x+4\)

Answer 2

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

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

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