When it comes to evaluating mathematical expressions, the process can sometimes seem daunting. With a string of numbers, symbols, and parentheses, it can be easy to get lost in the mix. However, with the help of proper formatting and understanding of the order of operations, even the most complex expressions can be easily evaluated. In this article, we will be focusing on the evaluation of the expression "3*(4+2)" and how it yields the integer value of 18.

First, let's break down the given expression. We have three numbers, 3, 4, and 2, and two symbols, the multiplication sign (*) and the addition sign (+). In order to evaluate this expression, we must follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

The first step in evaluating this expression is to simplify any expressions within parentheses. In this case, we have the expression "4+2" within parentheses. Since there are no exponents, we move on to the next step, which is to evaluate any multiplication and division. In our expression, we have a multiplication sign between the number 3 and the expression "4+2". This means we must first multiply 3 by 4, which gives us 12. The expression now becomes "3*12".

Next, we must evaluate the remaining addition within the expression. We simply add 12 to 2, giving us a final value of 14. Our expression now becomes "3*14".

Finally, we evaluate the multiplication between 3 and 14, giving us our final answer of 42. Therefore, "3*(4+2)" yields the integer value of 18.

It is important to note that without proper formatting and understanding of the order of operations, the answer to this expression could have been vastly different. For example, if we were to evaluate the expression without following the order of operations, we could end up with a completely different answer. Let's take a look at how this could happen.

If we were to simply evaluate the expression from left to right, we would first multiply 3 by 4, giving us 12. The expression now becomes "12+2", which gives us a final answer of 14. This is significantly different from the correct answer of 18.

In conclusion, evaluating mathematical expressions requires proper formatting and following the order of operations. In the case of "3*(4+2)", we must first simplify any expressions within parentheses, then evaluate any multiplication and division, and finally, evaluate any remaining addition and subtraction. By following these steps, we can confidently say that "3*(4+2)" yields the integer value of 18.