(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](/uploads/image/z/18832319-71-9.jpg?t=%28a%E5%8A%A0b%E5%8A%A0c%29%E7%9A%84%E7%AB%8B%E6%96%B9%2B%28b%E5%87%8Fa%E5%87%8Fc%29%E7%9A%84%E7%AB%8B%E6%96%B9%2B%28c%E5%87%8Fa%E5%87%8Fb%29%E7%9A%84%E7%AB%8B%E6%96%B9%2B%EF%BC%88a%E5%87%8Fb%E5%87%8Fc%EF%BC%89%E7%9A%84%E7%AB%8B%E6%96%B9%2C%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%2C%E8%B0%A2)
[(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
=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