Question

Answer 1

\(n\left(n+4\right)\left(n+5\right)\left(n+9\right)+100\\ =\left[n\left(n+9\right)\right]\left[\left(n+4\right)\left(n+5\right)\right]+100\\ =\left(n^2+9n\right)\left(n^2+9n+20\right)+100\\ =\left(n^2+9n+10-10\right)\left(n^2+9n+10+10\right)+100\\ =\left(n^2+9n+10\right)^2-100+100=\left(n^2+9n+10\right)^2\)

Answer 2

\(n\left(n+4\right)\left(n+5\right)\left(n+9\right)+100\)

\(=\left(n^2+9n\right)\left(n^2+9n+20\right)+100\)

\(=\left(n^2+9n\right)^2+20\left(n^2+9n\right)+100\)

\(=\left(n^2+9n+10\right)^2\) là số chính phương