Question

因式分解两则：(x-1)2+2(1-x)y+y2 ；X2+1/X2+2(X+1/X)+3

Answer 1

1.记x-1 = t,则原式 = t^2 - 2 t y + y^2.这下看出来了吧,完全平方式,分解得(t - y)^2,就是(x - 1 - y)^2.

2.注意到(x + 1/x)^2 = x^2 + 1/(x^2) + 2,再记x + 1/x = z,则原式 = z^2 + 2z + 1 = (z + 1)^2 = (x + 1/x + 1)^2.

注：^是乘幂符号,x^y是指x的y次幂.