how to simplify k(k+1)(k+2)+3(k+1)(k+2) to (k+1)(k+2)(k+3)?
To simplify the given expression, first expand each term:
k(k+1)(k+2) + 3(k+1)(k+2)
= k(k^2 + 2k + 1) + 3(k^2 + 2k + 2)
= k^3 + 2k^2 + k + 3k^2 + 6k + 6
= k^3 + 5k^2 + 7k + 6
Now, to factor out the common terms and simplify further, notice that (k+1)(k+2) can be factored out of each term:
= (k+1)(k+2)(k) + 3(k+1)(k+2)
= (k+1)(k+2)(k + 3)
Therefore, the simplified expression is (k+1)(k+2)(k+3).