化简求值:(x2+y2)(x2-y2)-(x+y)2(x-y)2,其中x=4,y=1.

问题描述:

化简求值:(x2+y2)(x2-y2)-(x+y)2(x-y)2,其中x=4,y=1.

原式=x4-y4-[(x+y)(x-y)]2=x4-y4-(x2-y22
=x4-y4-(x4-2x2y2+y4
=x4-y4-x4+2x2y2-y4=2x2y2-2y4
把x=4,y=1代入
原式=2×42×12-2×14=30.