Q:

How does $3\cdot 3^k - 3^k$ become $2 \cdot 3^k$?

Sorry for the really simple question. I am trying to help my kid with her SAT practice homework.
Step 1
$$3\cdot 3^k - 3^k = m$$
Step 2
$$2 \cdot 3^k = m$$
Step 3
$$3^k = \frac{m}{2}$$
I cannot grasp how they went from Step 1 to Step 2. Can someone please explain in the most basic steps possible? Thank you in advance.
Chris

A:

For equations like this, is can often help to replace the confusing part with a simpler variable - here we could say that $$3^k=A$$
Now we can rewrite the equation so that it is $$3\cdot A-A=m$$
Hopefully it is now quite easy to see that \begin{align}3\cdot A-A&=3\cdot A-1\cdot A\\
&=(3-1)\cdot A\\
&=2\cdot A\\
&=2\cdot 3^k\end{align}
You can also just think of it as "apples" - if you have $3$ apples and you take away one apple, then you are left with $2$ apples

