计算 (1)(a-b+c-d)(c-a-d-b); (2)(x+2y)(x-2y)(x4-8x2y2+16y4).
问题描述:
计算
(1)(a-b+c-d)(c-a-d-b);
(2)(x+2y)(x-2y)(x4-8x2y2+16y4).
答
(1)原式=[(c-b-d)+a][(c-b-d)-a]
=(c-b-d)2-a2
=c2+b2+d2+2bd-2bc-2cd-a2,
(2)∵x4-8x2y2+16y4=(x2-4y2)2
∴原式=(x2-4y2)(x2-4y2)2=(x2-4y2)3
=(x2)3-3(x2)2(4y2)+3x2•(4y2)2-(4y2)3
=x6-12x4y2+48x2y4-64y6.