Ta có \(n\left(n+3\right)\left(n+6\right)\left(n+9\right)+81\)
\(=n\left(n+9\right)\left(n+3\right)\left(n+6\right)+81\)
\(=\left(n^2+9n\right)\left(n^2+9n+18\right)+81\)
\(=\left(n^2+9n+9-9\right)\left(n^2+9n+9+9\right)+81\)
\(=\left(n^2+9n+9\right)^2-9^2+81\)
\(=\left(n^2+9n+9\right)^2\)
\(\Rightarrow n\left(n+3\right)\left(n+6\right)\left(n+9\right)+81\) là scp