问题标题:
计算:(1)(a+b)(a-b)(a4+a2b2+b4);(2)[(-ab+cd)(cd+ab)(a2b2+c2d2)+2a4b4](c4d4-a4b4).
问题描述:
计算:
(1)(a+b)(a-b)(a4+a2b2+b4);
(2)[(-ab+cd)(cd+ab)(a2b2+c2d2)+2a4b4](c4d4-a4b4).
刘延华回答:
(1)原式=(a2-b2)(a4+a2b2+b4)
=(a2)3-(b2)3
=a6-b6;
(2)原式=[-(ab-cd)(ab+cd))(a2b2+c2d2)+2a4b4](c4d4-a4b4)
=[-(a2b2-c2d2)(a2b2+c2d2)+2a4b4](c4d4-a4b4)
=(-a4b4+c4d4+2a4b4)(c4d4-a4b4)
=(c4d4+a4b4)(c4d4-a4b4)
=c8d8-a8b8.
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