3n(3n+3)(3n+6)(3n+9)+81的因式分解

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3n(3n+3)(3n+6)(3n+9)+81的因式分解3n(3n+3)(3n+6)(3n+9)+81的因式分解3n(3n+3)(3n+6)(3n+9)+81的因式分解3n(3n+3)(3n+6)(3

3n(3n+3)(3n+6)(3n+9)+81的因式分解
3n(3n+3)(3n+6)(3n+9)+81的因式分解

3n(3n+3)(3n+6)(3n+9)+81的因式分解
3n(3n+3)(3n+6)(3n+9)+81=(3n)^4+(3n)^3(3+6+9)+(3n)^2((6*9+3*6+3*9)+3n*(3*6*9)+81
=81n^4+486n^3+891n^2+486n+81
看来是我对因式分解出了点问题
3n(3n+3)(3n+6)(3n+9)+81=81{n(n+1)(n+2)(n+3)+1}
=81{(n^2+3n)(n^+3n+2)+1}=81(n^2+3n+1)^2
楼下是对的,现在成楼上的了

3n(3n+3)(3n+6)(3n+9)+81
=81n(n+1)(n+2)(n+3)+81
=81((n^2+3n)(n^2+3n+2)+1)
=81((n^2+3n)^2+2(n^2+3n)+1)
=81(n^2+3n+1)^2

3n(3n+3)(3n+6)(3n+9)+81
=81n(n+1)(n+2)(n+3)+81
=81[n(n+1)(n+2)(n+3)+1]
=81{[n(n+3)][(n+1)(n+2)]+1 }
=81[(n²+3n)(n²+3n+2)+1 ]
=81[(n²+3n)²+2(n²+3n)+1]
=3^4(n²+3n+1)²