1: \(x\left(1-x\right)+\left(x-1\right)^2\)
\(=x-x^2+x^2-2x+1=-x+1\)
2: \(\left(x-3\right)^2-x^2+10x-7\)
\(=x^2-6x+9-x^2+10x-7=4x+2\)
3: \(\left(x+2\right)^2-\left(x-3\right)\left(x+1\right)\)
\(=x^2+4x+4-\left(x^2-2x-3\right)\)
\(=x^2+4x+4-x^2+2x+3=6x+7\)
4: \(\left(x+4\right)\left(x+2\right)-\left(x-3\right)^2\)
\(=x^2+6x+8-x^2+6x-9\)
=12x-1