请老师解一下因式分解题：a3-b3+c3+3abc（注：a、b、c后的3为指数）.

Question

请老师解一下因式分解题：a3-b3+c3+3abc（注：a、b、c后的3为指数）.

Answer 1

a³-b³+c³+3abc
=(a³-3a²b+3ab²-b³)+c³+3a²b-3ab²+3abc
=(a-b)³+c³+3ab(a-b+c)
=(a-b+c)[(a-b)²-(a-b)c+c²]+3ab(a-b+c)
=(a-b+c)[(a-b)²-(a-b)c+c²+3ab]
=(a-b+c)[(a²-2ab+b²)-(a-b)c+c²+3ab]
=(a-b+c)(a²+b²+c²+ab+bc-ac)