已知F(X+Y,X-Y)=X^2*Y+X*Y^2,则F(X,Y)=?
问题描述：
已知F(X+Y,X-Y)=X^2*Y+X*Y^2,则F(X,Y)=?
答
令m= X+Y n=X-Y有X = (m+n)/2 Y = (m-n)/2代入F(X+Y,X-Y)=X^2*Y+X*Y^2得 F(m,n)= 1/4 * (m+n)^2 * (m-n)/2 + 1/4 * (m-n)^2 * (m+n)/2= 1/8 * [(m^2-n^2 )(m+n) + (m^2-n^2)(m-n)]= 1/8 * (m^2-n^2) * 2m= m(m^2-n^2...