Bài 4:
1) \(x\left(1-x\right)+\left(x-1\right)^2=x-x^2+x^2-2x+1=1-x\)
2) \(\left(x-3\right)^2-x^2+10x-7=x^2-6x+9-x^2+10x-7=4x+2\)
3)
\(\left(x+2\right)^2-\left(x-3\right)\left(x+1\right)\\
=x^2+4x+4-\left(x^2+x-3x-3\right)\\
=x^2+4x+4-x^2-x+3x+3\\
=6x+7\)
4) \(\left(x+4\right)\left(x-2\right)-\left(x-3\right)^2\)
\(=x^2-2x+4x-8-\left(x^2-6x+9\right)\\
=x^2+2x-8-x^2+6x-9\\
=8x-17\)
5) \(\left(x-2\right)^2+\left(x-1\right)\left(x+5\right)\)
\(=x^2-4x+4+x^2+5x-x-5=2x^2-1\)
6) \(\left(x+3\right)\left(x-3\right)-x\left(23+x\right)\)
\(=x^2-9-23x-x^2=-23x-9\)
7) \(\left(1-2x\right)\left(5-3x\right)+\left(4-x\right)^2\)
\(=5-3x-10x+6x^2+16-8x+x^2\\
=7x^2-21x+21\)
8) \(\left(x-2\right)\left(x+2\right)-\left(x-3\right)\left(x+1\right)\)
\(=x^2-4-\left(x^2+x-3x-3\right)\\
=x^2-4-x^2-x+3x+3\\
=2x-1\)