因式分解:(a-b)(3a+b)2+(a+3b)2(b-a).

问题描述:

因式分解:(a-b)(3a+b)2+(a+3b)2(b-a).

(a-b)(3a+b)2+(a+3b)2(b-a)
=(a-b)[(3a+b)2-(a+3b)2],
=(a-b)[9a2+b2+6ab-(a2+9b2+6ab)],
=(a-b)(8a2-8b2),
=8(a-b)(a2-b2),
=8(a-b)2(a+b).