a^4-b^4 - 4a^3(a-b)
=(a-b)(a+b)(a^2+b^2)-4a^3(a-b)
=(a-b)(a^3+b^3+ba^2+ab^2 - 4a^3)
=(a-b)[b^3-a^3 + a(b^2+ab-2a^2)]
=(a-b)[(b-a)(b^2+ab+a^2) + a(b-a)(b+2a)]
=(a-b)(b-a)[b^2+ab+a^2 + a(b+2a)]
=-(a-b)^2(b^2+2ab+3a^2)
=-(a-b)^2[(b+a)^2+2a^2]
因?yàn)閍不等于b,所以,(a-b)^2>0,(b+a)^2+2a^2>0,再有前面有負(fù)號(hào),所以
a^4-b^4 - 4a^3(a-b)