计算: (1)(a-2b+c)(a+2b-c)-(a+2b+c)2; (2)(x+y)4(x-y)4; (3)(a+b+c)(a2+b2+c2-ab-ac-bc).

问题描述:

计算:
(1)(a-2b+c)(a+2b-c)-(a+2b+c)2
(2)(x+y)4(x-y)4
(3)(a+b+c)(a2+b2+c2-ab-ac-bc).

(1)原式=a2-(2b-c)2-(a2+4b2+c2+4ab+4bc+2ac)
=a2-4b2-c2+4bc-a2-4b2-c2-4ab-4bc-2ac
=-8b2-2c2-4ab-2ac;
(2)原式=[(x+y)(x-y)]4
=(x2-y24
=x8+y8+6x4y4-4x6y2-4x2y6
(3)原式=a3+ab2+ac2-a2b-a2c-abc+a2b+b3+bc2-ab2-abc-b2c+a2c+b2c+c3-abc-ac2-bc2
=a3+b3+c3-3abc.