提公因式.

问题描述:

提公因式.
x^2y^2-x^2(y-1)^2
(a+b+c)^2-(a+b-c)^2

x^2y^2-x^2(y-1)^2=x^2[y^2-(y-1)^2]=x^2[y-(y-1)][y+(y-1)]=x^2[y-y+1][y+y-1]=x^2(2y-1)(a+b+c)^2-(a+b-c)^2 =[(a+b+c)+(a+b-c)][(a+b+c)-(a+b-c)]=[a+b+c+a+b-c][a+b+c-a-b+c]=2c(2a+2b)=4c(a+b)