化简: (1)(a-b)(a+b)3-2ab(a2-b2) (2)(a+b)(a2-ab+b2)-(a+b)3 (3)(a+4b-3c)2 (4)(a+4b-3c)(a-4b-3c)
问题描述:
化简:
(1)(a-b)(a+b)3-2ab(a2-b2)
(2)(a+b)(a2-ab+b2)-(a+b)3
(3)(a+4b-3c)2
(4)(a+4b-3c)(a-4b-3c)
答
(1)(a-b)(a+b)3-2ab(a2-b2)=(a-b)(a+b)3-2ab(a-b)(a+b)=(a-b)(a+b)[(a+b)2-2ab]=(a2-b2)(a2+b2)=a4-b4
(2)(a+b)(a2-ab+b2)-(a+b)3=(a+b)[(a2-ab+b2)-(a+b)2]=(a+b)(-3ab)=-3a2b-3ab2
(3)(a+4b-3c)2=[(a+4b)-3c]2=(a+4b)2-2(a+4b)•3c-(3c)2=a2+8ab+16b2-6ac-24bc-9c2
(4)(a+4b-3c)(a-4b-3c)=[(a-3c)+4b][(a-3c)-4b]=(a-3c)2-(4b)2=a2-6ac+9c2-16b2