a=二分之一m+1,b=二分之一m+2,c=二分之一m+3,求a^2+2ab+b^2-2ac+c^2-2bc

题目

a=二分之一m+1,b=二分之一m+2,c=二分之一m+3,求a^2+2ab+b^2-2ac+c^2-2bc

答案

a+b-c
=1/2m+1+1/2m+2-1/2m-3
=1/2m
a^2+2ab+b^2-2ac+c^2-2bc
=(a+b)^2-2(a+b)c+c^2
=(a+b-c)^2
=(1/2m)^2
=(1/4)m^2