题目内容
11、分解因式:(x4-4x2+1)(x4+3x2+1)+10x4=
(x+1)2(x-1)2(x2+x+1)(x2-x+1)
.分析:首先将x4+1看作一个整体,然后根据十字相乘法进行因式分解,得出结果.
解答:解:(x4-4x2+1)(x4+3x2+1)+10x4,
=[(x4+1)2-x2(x4+1)-12x4]+10x4,
=(x4+1)2-x2(x4+1)-2x4,
=(x4+1-2x2)(x4+1+x2),
=(x2-1)2[(x2+1)2-x2],
=(x+1)2(x-1)2(x2+x+1)(x2-x+1).
故答案为:(x+1)2(x-1)2(x2+x+1)(x2-x+1).
=[(x4+1)2-x2(x4+1)-12x4]+10x4,
=(x4+1)2-x2(x4+1)-2x4,
=(x4+1-2x2)(x4+1+x2),
=(x2-1)2[(x2+1)2-x2],
=(x+1)2(x-1)2(x2+x+1)(x2-x+1).
故答案为:(x+1)2(x-1)2(x2+x+1)(x2-x+1).
点评:本题综合考查了十字相乘法和整体思想,解题的关键是将x4+1看作一个整体.
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