Question

阅读下面两例题的分解因式的过程，并回答问题

1+ax+ax(1+ax) 1+ax+ax(1+ax)+ax(1+ax)²
=(1+ax)(1+ax) =(1+ax)(1+ax)(1+ax)²
=(1+ax)² =(1+ax)²+ax(1+ax)²
=(1+ax)²(1+ax)
=(1+ax)³
分解因式：x-1-x(x-1)+x(x-1)²-x(x-1)³+···-x(x-1)²º¹³+x(x-1)^2014

Answer 1

原式=(x-1)[1-x+x(x-1)-x(x-2)²+....x(x-1)²º¹⁴]=(x-1)(x-1)[-1+x-x(x-1)+x(x-1)²-x(x-1)³+···+x(x-1)²º¹³]
=···
=(x-1)²º¹³*[1-x+x(x-1)]
=(x-1)²º¹⁴*(-1+x)
=-(x-1)^2015

Answer 2

原式
=(x-1)[1-x+x(x-1)-x(x-1)^2+···+x(x-1)^2014]
=(x-1)(x-1)[-1+x-x(x-1)+x(x-1)^2-x(x-1)^3+···+x(x-1)^2013]
=···
=(x-1)^2014*[1-x+x(x-1)]
=(x-1)^2015*(-1+x)
=(x-1)^2016

Answer 3

原式=(x-1)[1-x+x(x-1)-x(x-2)²+....x(x-1)²º¹⁴]=(