Is there an order of operations when simplifying algebra?

Question

My brain is getting all twisted from trying to simplify algebra. I'll use a simple example:

4(3x-2)4*2

I understand that the distributive property has to be used here. We are taught to work from left to right by starting with parenthesis, exponents, multiplication, division, addition, and finally subtraction. Since doing the distributive property requires multiplication, shouldn't I be starting off with 4*3x and 4*-2? I know that's wrong, but I keep thinking it's the right way to go. Does anyone have any good tips that help in simplifying or some good rules that can stop me from making mistakes?

Answer 1

4(3x - 2)4*2

first the distribution

(12x - 8)4*2

next the 2nd distribution

since a(b + c) = (b +c)a

(48x - 32)*2

then the third distribution

===== 96x - 64

Answer 2

Excellent question: Here is what you need to remember to solve something like this:

It is ok for you to do "4*3x and 4*-2" but you need to remember to keep the parenthesis because the 4,4 and 2 that are outside the parenthesis are multiplications. (If they were additions then it would be simple distributive property multiplication inside the parenthesis) but since the numbers outside are multiplications you should either do 4*4*2 first or keep the parenthesis as follows

4(3x-2)4*2
= (12x-8)4*2
= (48x-32)*2
= 96x-64

OR

=4*4*2(3x-2)
=32(3x-2)
=96x-64

Hope this hellps!

Answer 3

4(3x-2)4*2
Here there are 4 terms in which 3 are natural numbers. So multiply the three numbers first then go to open the brackets.
You can do the above problem as follows:
4(3x-2)4*2
=4*4*2(3x-2)
= 32(3x-2)
=32*3x-32*2
=96x-64
Now you got 2 terms out of 1.
As in multiplication & division, any number of terms will be considered as a single term.
ex: 2*5*6*3x = 180x

Answer 4

The order of operations is to compute

1. Parentheses, skipping over exponents, mult and div, add and subtract.
2. Exponents, skipping over mult and div, add and subtract
3. multiplication and division in the order they occur from left to right, skipping over add and subtract.
4. adding and subtracting in the order they occur.

To do the problem you posted, do the exponent first, then multiply the 4 through the parentheses, and finally multiply the 16 (from the 4 squared) through the result 12x - 8 from multiplying the 4 through the parentheses.