化简2x的四次方—2X的三次方—X的二次方+1
问题描述：
化简2x的四次方—2X的三次方—X的二次方+1
要过程
= (x-1)[2x^3 - 2x^2 + 2x^2 - 2x + x - 1]
= (x-1)[(x-1)(2x^2 + 2x + 1)]
没看懂
答
2x^4 - 2x^3 - x^2 + 1= 2x^3[x - 1] - [x^2 - 1]= 2x^3(x - 1) - (x - 1)(x + 1)= (x-1)[2x^3 - x - 1]= (x-1)[2x^3 - 2x^2 + 2x^2 - 2x + x - 1]= (x-1)[(x-1)(2x^2 + 2x + 1)]= (x-1)^2[2x^2 + 2x + 1]