Question

一道因式分解题

a³-6a²b+12ab²-8b³
a³+b³+3ab²+3a²b
快啊~~~~~~~~~~~求知识

Answer 1

a³-6a²b+12ab²-8b³
=a³-8b³-6a²b+12ab²
=(a-2b)(a+2ab+4b²)-6ab(a-2b)
=(a-2b)(a-4ab+4b²）
=(a-2b)³

a³+b³+3ab²+3a²b
=(a+b)(a²-ab+b²)+3ab(a+b)
=(a+b)(a²+2ab+b²)
=(a+b)³

Answer 2

你好，解答如下：
a³-6a²b+12ab²-8b³
=a(a^2-6ab+8b^2)+4b^2(a-2b)
=a(a-2b)(a+4b)+4b^2(a-2b)
=(a-2b)(a^2-4ab+4b^2)
=(a-2b)^3

a³+b³+3ab²+3a²b
=(a+b)(a²+b²-ab)+3ab(a+b)
=(a+b)(a²+b²+2ab)
=(a+b)³

Answer 3

a³-6a²b+12ab²-8b³
=[a³-(2b)³]-6ab(a-2b)
=(a-2b)(a² +2ab+4b²) -6ab(a-2b)
=(a-2b)(a² -4ab+4b²)
=(a-2b)³
a³+b³+3ab²+3a²b
=(a+b)³

Answer 4

a3-6a2b+12ab2-8b3 =(a-2b)3
a3+b3+3ab2+3a2b=(a+b)3