因式分解(a的2次方-b的2次方-c的2次方)的2次方-4b的2次方c的2次方怎样算

题目

因式分解(a的2次方-b的2次方-c的2次方)的2次方-4b的2次方c的2次方怎样算

答案

(a²-b²-c²)²-4b²c²
=(a²-b²-c²)²-(2bc)²
=[(a²-b²-c²)+2bc][(a²-b²-c²)-2bc]
=[a²-(b²-2bc+c²)][a²-(b²+2bc+c)²]
=[a²-(b-c)²][a²-(b+c)²]
=[a+(b-c)][a-(b-c)][a+(b+c)][a-(b+c)]
=(a+b-c)(a-b+c)(a+b+c)(a-b-c)
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