Factorization of $a^{dq+r}-1$.

Question

So I'm having trouble with factorizing:

$$a^{dq+r} - 1$$.

I'm aware that $a^n - 1$ factorizes to $(a - 1)(a^{n-1} + a^{n-2}+\ldots +a+1)$.

So I assume that the correct answer must be $(a^{dq}-1)(a^{dq+r-1} +\ldots +a^{dq}+1)$.