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怎样把n^4+2n^3+3n^2+2n+1因式分解成n*(n+1)+1)^2?

分类: 作业答案 • 2023-01-20 06:38:23
问题描述：

怎样把n^4+2n^3+3n^2+2n+1因式分解成n*(n+1)+1)^2?

答

n^4+2n^3+3n^2+2n+1
=n^4+2n^3+n^2+2n^2+2n+1
=n^2(n^2+2n+1)+2n(n+1)+1
=n^2(n+1)^2+2n(n+1)+1
=[n(n+1)+1]^2

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