Question

Prove that for all whole values of n the value of the expression:
n(n–1)–(n+3)(n+2) is divisible by 6.

Answer 1

Explanation:

Multiply it out.

n^2 -n -(n^2 +5n+6)

= -6n -6

= -6(n +1)

For any integer value of n, this is divisible by 6. (The quotient is -(n+1).)