题目内容
在有理数范围内分解因式:(x+y)4+(x2-y2)2+(x-y)4=________.
(3x2+y2)(x2+3y2)
分析:先补项+(x+y)2(x-y)2-(x+y)2(x-y)2,后根据完全平方公式进行计算,再根据平方差公式分解即可.
解答:原式=(x+y)4+(x+y)2(x-y)2+(x-y)4+(x+y)2(x-y)2-(x+y)2(x-y)2,
=[(x+y)2+(x-y)2]2-[(x+y)(x-y)]2,
=[(x+y)2+(x-y)2+(x+y)(x-y)][(x+y)2+(x-y)2-(x+y)(x-y)],
=(3x2+y2)(x2+3y2)
故答案为:(3x2+y2)(x2+3y2).
点评:本题考查了分解因式的应用,方法是采用拆项和分组后能用公式法分解因式.
分析:先补项+(x+y)2(x-y)2-(x+y)2(x-y)2,后根据完全平方公式进行计算,再根据平方差公式分解即可.
解答:原式=(x+y)4+(x+y)2(x-y)2+(x-y)4+(x+y)2(x-y)2-(x+y)2(x-y)2,
=[(x+y)2+(x-y)2]2-[(x+y)(x-y)]2,
=[(x+y)2+(x-y)2+(x+y)(x-y)][(x+y)2+(x-y)2-(x+y)(x-y)],
=(3x2+y2)(x2+3y2)
故答案为:(3x2+y2)(x2+3y2).
点评:本题考查了分解因式的应用,方法是采用拆项和分组后能用公式法分解因式.
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