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

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

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

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(n+1)]²+2n(n+1)+1
=[n(n+1)+1]²

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