先化简 再求值【(x平方+y平方)的平方-4x平方y平方】/(x+y)平方

问题描述:

先化简 再求值【(x平方+y平方)的平方-4x平方y平方】/(x+y)平方

【(x²+y²)²-4x²y²】/(x+y)²
=(x²+y²+2xy)(x²+y²-2xy)/(x²+y²+2xy)
=x²+y²-2xy

=[(x4+2x2y2+y4)-4x2y2]/(x+y)2
=[x4-2x2y2+y4]/(x+y)2
=[(x2-y2)2]/(x+y)2
=[(x-y)(x+y)]2/(x+y)2
=(x-y)2

原式=(x²+y²+2xy)(x²+y²-2xy)/(x+y)²
=(x+y)²(x-y)²/(x+y)²
=(x-y)²