2b2c2+2c2a2+2a2b2-a4-b4-c4

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2b2c2+2c2a2+2a2b2-a4-b4-c4

2b2c2+2c2a2+2a2b2-a4-b4-c4
2b2c2+2c2a2+2a2b2-a4-b4-c4

2b2c2+2c2a2+2a2b2-a4-b4-c4
因为
a4+b4+c4-2a2b2-2b2c2-2c2a2
=(a2-b2-c2)2-4b2c2
=(a2-b2-c2+2bc)(a2-b2-c2-2bc)
=(a2-(b-c)2)(a2-(b+c)2)
=(a+b-c)(a-b+c)(a+b+c)(a-b-c)
所以
2b2c2+2c2a2+2a2b2-a4-b4-c4
=-(a+b-c)(a-b+c)(a+b+c)(a-b-c)

2b2c2+2c2a2+2a2b2-a4-b4-c4
=(a+b-c)(a-b+c)(a+b+c)(b+c-a)
供参考!JSWYC