Question

Prove that a factor of ${\left(2n+3\right)}^2-{\left(2n-3\right)}^2$ is 8, where $n$ is a natural number.

Answer 1

given

$\Rightarrow (2n+3{)}^2-(2n-3{)}^2$

$\Rightarrow 4n^2+9+12n-4n^2-9+12n$

$\Rightarrow 24n$

$\Rightarrow 8\left(3n\right)$ proved

So we can observe that $8$ is a factor of the above eqn.