Is the mathematical statement $(a+4)(a+2)=a^2+8$ correct? given the reasons to support your answer.

The given mathematical statement is $\left(a+4\right)\left(a+2\right)=a^2+8$.

Simplifying the LHS of $\left(a+4\right)\left(a+2\right)=a^2+8$

$\left(a+4\right)\left(a+2\right)=a^2+2a+4a+8$

$=a^2+6a+8$

$\ne \mathrm{RHS}$

Therefore, the given mathematical statement is not correct.