Question

因式分解(x^2-2x)^2-(2x-x^2)+1

谢谢啊~~原来是我们老师抄错了，麻烦大家了

Answer 1

错了
应该是(x^2-2x)^2-2(2x-x^2)+1
=(x^2-2x)^2+2(x^2-2x)+1
=(x^2-2x+1)^2
=(x-1)^4

Answer 2

(x²-2x)²-(2x-x²)+1
=(x²-2x)²+(x²-2x)+1
=(x²-2x)²+(x²-2x)+1/4+3/4
=(x²-2x+1/2)²+3/4
=(x²-2x+1-1/2)²+3/4
=[(x-1)²-1/2]+3/4

(x²-2x)²-2(2x-x²)+1
=(x²-2x)²+2(x²-2x)+1
=(x²-2x+1)²
=(x-1)^4

Answer 3

(x^2-2x)^2-2(2x-x^2)+1 =(x^2-2x)^2+2(x^2-2X)+1=(x^2-2x+1)^2=(x+1)^4