求证:(x+y)^3+3xy(1-x-y)-1=(x+y-1)(x^2+y^2-xy+x+y+1)
题目
求证:(x+y)^3+3xy(1-x-y)-1=(x+y-1)(x^2+y^2-xy+x+y+1)
答案
(x+y)^3+3xy(1-x-y)-1
=(x+y)^3-1+3xy(1-x-y)
=(x+y-1)(x^2+2xy+y^2+x+y+1)-3xy(x+y-1)
=(x+y-1)(x^2+2xy+y^2+x+y+1-3xy)
=(x+y-1)(x^2+y^2-xy+x+y+1)
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