高校问答烟台莱山的楼盘:一道数学题
来源：百度文库 编辑：高校问答 时间：2024/04/29 16:45:13
计算：
(-xy+1)(xy+1)(x^2 y^2+1)(要步骤)
(-xy+1)(xy+1)(x^2 y^2+1)(要步骤)
(-xy+1)(xy+1)(x^2 y^2+1)
= -(xy-1)(xy+1)(x^2y^2+1)
= -(x^2y^2-1)(x^2y^2+1)
= 1-x^4y^4
(1-x^2y^2)(x^2 y^2+1)=1-x^4y^4
(-xy+1)(xy+1)(x^2 y^2+1)
=-（xy-1）（xy+1）(x^2 y^2+1)
=-（x^2 y^2-1^2）(x^2 y^2+1)
=-（x^4y^4-1)
=-x^4y^4+1
=1-x^4y^4
解：原式=(1-xy)(1+xy)(x^2 y^2+1)
=(1-x^2y^2)(1+x^2 y^2)
=1-x^4y^4
注：先观察，发现将原式稍微变下形，然后直接使用平方差公式即可。
(-xy+1)(xy+1)(x^2 y^2+1)
=-（xy-1）（xy+1）(x^2 y^2+1)
=-（x^2 y^2-1^2）(x^2 y^2+1)
=-（x^4y^4-1)
=-x^4y^4+1
=1-x^4y^4
解：原式=(1-xy)(1+xy)(x^2 y^2+1)
=(1-x^2y^2)(1+x^2 y^2)
=1-x^4y^4