(a加b加c)的立方+(b减a减c)的立方+(c减a减b)的立方+(a减b减c)的立方,因式分解,谢

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(a加b加c)的立方+(b减a减c)的立方+(c减a减b)的立方+(a减b减c)的立方,因式分解,谢

(a加b加c)的立方+(b减a减c)的立方+(c减a减b)的立方+(a减b减c)的立方,因式分解,谢
(a加b加c)的立方+(b减a减c)的立方+(c减a减b)的立方+(a减b减c)的立方,因式分解,谢

(a加b加c)的立方+(b减a减c)的立方+(c减a减b)的立方+(a减b减c)的立方,因式分解,谢
[(a+b+c)³+(b-a-c)³]+[(c-a-b)³+(a-b-c)³]
=2b[(a+b+c)²+(a+b+c)(a-b+c)+(a-b+c)²]-2b[(a+b-c)²+(a+b-c)(a-b-c)+(a-b-c)²]
=2b[(a+b+c)²+(a+b+c)(a-b+c)+(a-b+c)²-(a+b-c)²-(a+b-c)(a-b-c)-(a-b-c)²]
=2b﹛[(a+b+c)²-(a+b-c)²]+[(a+b+c)(a-b+c)-(a+b-c)(a-b-c)+[(a-b+c)²-(a-b-c)²]﹜
=2b﹛(2(a+b)﹙2c﹚+[﹙a+c﹚²-b²]-[﹙a-c﹚²-b²]+2(a-b)(2c)﹜
=2b﹛[(a+b)+(a-b)]4c+[﹙a+c﹚²-﹙a-c﹚²]
=2b﹙8ac+4ac﹚
=24abc