百度作业网计算 （1）[(x+2)(x-2)]^2 （2）(x+2y-3)(x-2y+3)(3)(x+y)^2(x-y)^2-(x
来源：学生作业帮 编辑：百度作业网作业帮 分类：数学作业 时间：2024/06/01 17:06:15
计算 （1）[(x+2)(x-2)]^2 （2）(x+2y-3)(x-2y+3)(3)(x+y)^2(x-y)^2-(x-y)(x+y)(x^2+y^2)
![计算 （1）[(x+2)(x-2)]^2 （2）(x+2y-3)(x-2y+3)(3)(x+y)^2(x-y)^2-(x](/uploads/image/z/19846082-2-2.jpg?t=%E8%AE%A1%E7%AE%97+%EF%BC%881%EF%BC%89%5B%28x%2B2%29%28x-2%29%5D%5E2+%EF%BC%882%EF%BC%89%28x%2B2y-3%29%28x-2y%2B3%29%283%29%28x%2By%29%5E2%28x-y%29%5E2-%28x)
计算 （1）[(x+2)(x-2)]^2 =[x^2-4]^2=x^4-8x^2+16
（2）(x+2y-3)(x-2y+3)=[x+(2y-3)][x-(2y-3)]=x^2-(2y-3)^2=x^2-4y^2+12y-9
(3)(x+y)^2(x-y)^2-(x-y)(x+y)(x^2+y^2)
=(x+y)(x-y)[(x+y)(x-y)-x^2-y^2]
=(x^2-y^2)*(-2y^2)
=2y^4-2x^2y^2
（2）(x+2y-3)(x-2y+3)=[x+(2y-3)][x-(2y-3)]=x^2-(2y-3)^2=x^2-4y^2+12y-9
(3)(x+y)^2(x-y)^2-(x-y)(x+y)(x^2+y^2)
=(x+y)(x-y)[(x+y)(x-y)-x^2-y^2]
=(x^2-y^2)*(-2y^2)
=2y^4-2x^2y^2
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