Why is $4^{n+1} -1 = 4^n - 1 + 3 * 4^n$?

Question

I'm learning about proving equations using induction using an online tutorial, but I'm stuck at this step:

$$4 * 4^n-1 = 4^n - 1 + 3 * 4^n$$

I don't know how the author turned the $4$ into $3 * 4^n$. I tried to remove the 4 by multiplying with $\frac{1}{4}$:

$$(4 * 4^n - 1) * \frac{1}{4}$$ $$= 4^n - \frac{1}{4}$$

But now I'm stuck. So my question is, what are the steps necessary to turn $4 * 4^n - 1$ into $4^n - 1 + 3 * 4^n$?

Answer 1

$$4(4^n)-1=[3(4^n)+(1)(4^n)]-1=3(4^n)+[(1)(4^n)-1]$$

Answer 2

For any $x$, its true that $4x-1 = x-1 + 3x$