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My son was assigned a homework where he had to simplify the following expression:

$$(3x+2)\cdot2\cdot25\cdot2 \div 50 - (x+4)$$

I believe that they want him to first multiply 25.2 and then divide by 50 to obtain:

$$(3x+2)\cdot2 - (x+4)$$

and then simplify from there. However, if you were to follow the order of operations, the first step is to remove the parenthesis and it is not clear to me how one would remove the parenthesis for $(3x+2)$.

Can someone help out?

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    $(3x+2) 2 - (x+4) = (6x+4)-(x+4) = 6x+4-x-4 = 6x-x=5x$. – 2017-02-08
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    Are you sure about $25.2$ ? Isn't it $25\cdot2$ ? – 2017-02-08
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    @YvesDaoust Looking at the original format of the question, it had `(3x+2).2.25.2`, in which it seems `.` was consistently intended to be multiplication. The edit failed to convert one of the dots. I have attempted to fix that. – 2017-02-08

2 Answers 2

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In the order of operations, the first step is removing parenthesis. However this is necessary only if the terms within parenthesis can be simplified further which is not true in this case. Opening parenthesis implies simplifying the terms within parenthesis first. Therefore in your problem there is no need for opening parenthesis and your solution is correct.

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When the objects inside the parentheses are unlike terms, you cannot simplify inside the parentheses any further. You treat the parenthesis as a single object and simplify the other operations in order until you get another single object multiplied by the parenthesis. Then you apply the distributive law a(b + c) = ab + ac (You know this well already; for example 5 x \$1.20 = 5 x \$1 + 5 x \$0.20 = \$5 + \$1.00 = \$6)

So the above answers are correct and show the correct order of simplification.