已知x+y=2 求(x²-y²)²-8(x²+y²)的值

已知x+y=2 求(x²-y²)²-8(x²+y²)的值
已知x+y=2 求(x²-y²)²-8(x²+y²)的值

已知x+y=2 求(x²-y²)²-8(x²+y²)的值
(x²-y²)²-8(x²+y²)
=(x+y)^2(x-y)^2-8(x²+y²)
=4(x-y)^2-8(x²+y²)
=4x^2+4y^2-8xy-8x^2-8y^2
=-4(x^2+y^2+2xy)
=-4(x+y)^2
=-16