Use the distributive property to remove the parentheses 
in the following expression.  Then simplify your result 
if possible.

	10(8 + 4)


The PEMDAS rule says we have to do all operations inside 
parentheses before we can multiply.

However, the DISTRIBUTIVE PROPERTY allows us to VIOLATE 
the PEMDAS rule to a certain extent!!!

It allows us to multiply first WITHOUT doing the operations
of addition or subtraction inside the parentheses first.

However, when we use the DISTRIBUTIVE PROPERTY we must 
multiply by every term inside the parenthesesw.

To demonstrate the DISTRIBUTIVE PROPERTY in your example 
we do not have to add the 8 and the 4 in the parentheses 
first.

Instead we can multiply the 10 by BOTH the 8 and the 4. 

	10(8 + 4)    =

      10(8) + 10(4)  =

         80 + 40     =

           120 

That's the answer.  You can check it by using PEMDAS, where
we must do the addition inside the parentheses first:

        10(8 + 4)

         10(12)

          120

We get the same answer using PEMDAS that we get when we use
the DISTRIUTIVE PROPERTY.  

Now you may wonder why we need to learn the DISTRIBUTIVE 
PROPERTY since we can just use PEMDAS, and PEMDAS is 
easier. 

The answer is that in algebra where we have 
unknowns like x sometimes we CANNOT add what is inside 
the parentheses, as in the expression 10(8 + x).

We CANNOT add the 8 and the x because x is unknown. 
However we can use the DISTRIBUTIVE PROPERTY and get 
rid of the parentheses:

	10(8 + x)    =

      10(8) + 10(x)  =

         80 + 10x      

And so the DISTRIBUTIVE PROPERTY allows us to at least
eliminate the parentheses even when we can't add the
terms inside them.

Edwin