This is where you're incorrect.
Factoring is merely the process of multiplying something into parenthesis or dividing something out of the parenthesis, and parenthesis are used to group terms within.
So using a * as a multiplication symbol would not stop something from factoring into parenthesis.
Let's look at both of these individually:
We start with: 48/2(9+3)
The first thing to notice is that 48 is being divided by 2:
48/2(9+3)
2 goes in to 48 24 times, so now we have:
24(9+3)
Now we can factor 24 into the parenthesis: (
24*9+
24*3)
Next, we finish multiplying: (216+72)
By adding the two, we get: 288
Now onto the second version: 48/2*(9+3):
Here, the first thing we notice is also that 48 is being divided by 2:
48/2*(9+3)
2 still goes in to 48 24 times, so now we have:
24(9+3)
Now we can multiply 24 into the parenthesis: (
24*9+
24*3)
Next, we finish multiplying: (216+72)
By adding the two, we get: 288
How about if we start with the parenthesis first?:
We have: 48/2*(9+3) or 48/2(9+3)
This time, we start with the terms in the parenthesis first and add 9 to 3: 48/2(12) or 48/2*(12)
Next, we notice that once again there is a 48 being divided by 2, and we already know what that means: 24(12) or 24*(12)
Now by factoring or multiplying the 24 in we get the product: 288 or 288
So it can be said conclusively that 48/2(9+3) is the same as 48/2 * (9+3) and that both equal 288.
That's it for this addition of Math with fiat.