Question

If $n$ is a whole number greater than 1, then $n^2(n^2-1)$ is always divisible by:

• A. $12$
• B. $12$ and $24$
• C. $24$
• D. $36$

Answer 1

The correct option is A $12$

If n is whole number greater than 1 then the least value of n will be

$n=2,3,4,\mathrm{5.......}$

Now given that $n^2(n^2-1)$

$n^2(n+1)(n-1)$..........($a^2-b^2=(a+b)(a-b)$)

least value for n =2. now put it given expression

$2^2(2+1)(2-1)$

$4\times 3\times 1=12$

hence the expression always will be divisible by $12$

hence option $A$ is correct.