So this is the expression I don't understand how to simplify $$3^{n+1}-3+2\cdot 3^{n+1}$$ Simplified, it should be $$3\cdot 3^{n+1}-3$$
I have a problem in understanding where the other $ 3^{n+1}$ disappears and how we get $3 \cdot$
Could someone explain this to me with concrete examples?
It's easy. Let's take it step-by-step: \begin{align} \underbrace{3^{n+1}}-3 + 2 \cdot \underbrace{3^{n+1}}_{\text{}} &=\\ &= 3^{n+1} \cdot (1 + 2) - 3\\ &= 3 \cdot 3^{n+1} - 3\\ \end{align} which by your claim ends your question. However, this can be simplified even further when you see that \begin{align} \underbrace{3} \cdot 3^{n+1} - \underbrace{3} = 3 \cdot (3^{n+1} - 1). \end{align}