SOLUTION: Discuss why the expressions (8x / 4x), 8x � 4x and (8x)�(4x) are not equivalent?

Question 819881: Discuss why the expressions (8x / 4x), 8x � 4x and (8x)�(4x) are not equivalent?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
(8x / 4x), 8x � 4x and (8x)�(4x)
It will help if we insert a multiplication symbol into the expressions to replace the implied multiplications:
(8*x/4*x), 8*x�4*x and (8*x)�(4*x)

Next, as always, we should follow the order of operations (aka PEMDAS). And the order of operations, when it comes to multiplication and division, says that multiplying and dividing should be done from left to right. So for (8*x/4*x)
we work from left to right. So we start by multiplying 8 and x:
(8x/4*x)
Then we divide 8x by 4:
(2x*x)
And then 2x * x:

For 8*x�4*x we again work from left to right. First 8 times x:
8x�4*x
Then 8x divided by 4:
2x*x
and then 2x times x:

For (8*x)�(4*x), because of the parentheses around the 8*x and 4*x, the order of operations tells us to do the two multiplications first:
(8x)�(4x)
Then we divide. The x's cancel and 8 divided by 4 is:
2

So you can now see that the first two expressions are equivalent but the third one is different.
RELATED QUESTIONS
Discuss why the expressions , and (8x) (4x) are not equivalent? (answered by Fombitz)

8x^=4x (answered by ikleyn)

4x�4x+... (answered by Awesom3guy)

8x=34-4x (answered by checkley71,tutorcecilia)

Solve:... (answered by jim_thompson5910)

8x =4x(squared)... (answered by stanbon)

... (answered by checkley77)

{{{8x-12=15x-4x}}} (answered by College Student)

-8x - 4x =... (answered by persian52)