化简: (1)a4(x-y)2+2a2(y-x)2+(x-y)2; (2)8(a2-b2)(a-b)-2(a+b)3
问题描述:
化简:
(1)a4(x-y)2+2a2(y-x)2+(x-y)2;
(2)8(a2-b2)(a-b)-2(a+b)3
答
(1)原式=(x-y)2(a4+2a2+1),
=(x-y)2(a2+1)2;
(2)原式=8(a+b)(a-b)(a-b)-2(a+b)3,
=2(a+b)[4(a-b)2-(a+b)2],
=2(a+b)(3a-b)(a-3b).