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When solving mathematical problems, it's essential to understand the basic arithmetic operations such as addition, subtraction, multiplication, and division. Each operation has its own set of rules that must be followed to get the correct answer. In the context of our exercise, we focus on multiplication, which is one of the fundamental operations in arithmetic.

Multiplication can be seen as repeated addition. For instance, multiplying two by three (\(2 \times 3\)) is the same as adding two, three times (\(2 + 2 + 2\)). The sign of the numbers being multiplied can affect the outcome significantly. A positive number multiplied by a positive yields a positive result, similar to a negative times a negative. However, a positive number multiplied by a negative, or vice versa, will always result in a negative answer. Understanding this concept is crucial when dealing with expressions like the one in our exercise, where both positive and negative numbers are present.

Multiplication has several properties that can make calculations easier and more intuitive. One such property is the commutative property, which states that the order of the numbers does not affect the product: \(a \times b = b \times a\). This property allows us to reorder the numbers in our given expression to simplify our work.

Next, the associative property tells us that no matter how we group the numbers, the product will be the same: \( (a \times b) \times c = a \times (b \times c) \). In the exercise, we grouped negative numbers together to use another important concept – the rule that the product of two negative numbers is a positive. Additionally, the identity property of multiplication states that any number multiplied by one remains unchanged, which lets us disregard the 'one' in our calculation. These properties collectively enable us to simplify and strategically approach multiplication problems.

The goal of simplifying expressions is to make them as straightforward as possible. This often involves grouping like terms, using multiplication properties, and reducing the expression to fewer terms without changing its value.

In our exercise, we firstly grouped the negative numbers and utilized the knowledge that a negative times a negative is a positive. This simplified our expression from a mix of negative and positive numbers to only positive ones. The next step was to multiply these positive numbers together. Multiplying by one is unnecessary as it doesn't change the value, which is a handy simplification tactic. We also combined numbers that are easier to multiply, like 2 and 10, before tackling the other factors. By following these strategies, we turned a slightly complex expression into a simple single positive number, showcasing the power of effectively simplifying expressions.