一道高等数学题,帮忙做一下!

s=x+y,t=x-y
x=(s+t)/2,y=(s-t)/2

f(x+y,x-y)=xy+y^2=y(x+y)=[(s-t)/2]*s
f(s,t)=(s^2-st)/2
f(x,y)=(x^2-xy)/2

设
x+y=a
x-y=b 所以：
x=（a+b）/2
y=（a-b）/2
f(x+y,x-y)=xy+y*y就变成f(a,b)=(a+b)/2*(a-b)/2+(a-b)(a-b)/4

f(a,b)=(a*a-b*b+a*a-2ab+b*b)/4
f(a,b)=(a*a-a*b)/2
也就是f（x，y）=（x*x-x*y）/2

则f(x+y,x-y)=xy+y*y 等于

fx+fy, f x-fy = xy+y*y

f(x,y)=xy+y*y - fx+fy

f(x,y)=y(x+y)-f(x-y)

所以f(x+y,x-y)=xy+y*y,则f(x,y)=_y(x+y)-f(x-y)__