1/2(x^2+y^2)^2-2X^2y^2

来源：百度知道编辑：UC知道时间：2024/06/24 09:30:35

1/2(x^2+y^2)^2-2X^2y^2怎么做啊，要过程

是要因式分解么?

原式=1/2[(x^2+y^2)^2-4x^2y^2]

=1/2[(x^2+y^2)^2-(2xy)^2]

=1/2[(x^2+y^2+2xy)(x^2+y^2-2xy)]

=1/2(x+y)^2(x-y)^2

换元令x^2=m y^2=n
最后得0.5（m-n）^2
0.5（x-y）^2（x+y）^2

1/2(x^2+y^2)^2-2X^2y^2
=(1/2)(x^4+2x^2y^2+y^4-4x^2y^2)
=(1/2)(x^4-2x^2y^2+y^4)
=(1/2)*(x^2-y^2)^2
=(1/2)(x+y)^2(x-y)^2

1/2(x^2+y^2)^2-2X^2y^2
=1/2[(x^2+y^2)^2-4X^2y^2]
=1/2(x^2-y^2)^2

1/2(x^2+y^2)^2-2X^2y^2
=1/2【(x^2+y^2)^2-4X^2y^2)】
=1/2(x^2+y^2+2X^2y^2)(x^2+y^2-2X^2y^2)
=1/2(x+y)^2*(x-y)^2

1/2(x^2+y^2)^2-2X^2y^2
=(1/2)(x^4+2x^2y^2+y^4-4x^2y^2)
=(1/2)(x^4-2x^2y^2+y^4)
=(1/2)*(x^2-y^2)^2
=(1/2)(x+y)^2(x-y)^2
这个方法还可以·······