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计算:(x+y+z)(-x+y+z)(x-y+z)(x+y-z).
人气:236 ℃ 时间:2020-09-26 02:37:00
解答
原式=[(y+z)+x][(y+z)-x][x-(y-z)][x+(y-z)]
=[(y+z)2-x2][x2-(y-z)2]
=(y2+2yz+z2-x2)(x2-y2-z2+2yz)
=[2yz+(y2+z2-x2)][2yz-(y2+z2-x2)]
=(2yz)2-(y2+z2-x22
=4y2z2-y4-z4-x4-2y2z2+2x2y2+2x2z2
=-x4-y4-z4+2y2z2+2x2y2+2x2z2
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