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Mathematical multiplication is a fundamental arithmetic operation that finds the product of two numbers. It's like adding a number to itself a certain number of times. For example, when you multiply 8 by 2, it means you are adding 8 twice: 8 + 8, which equals 16.

This idea makes multiplication a quick way to handle repeated addition. Especially when working with larger numbers or variables, multiplication is a core part of simplifying and solving problems. In expressions like \(8(2+9)\), multiplication helps us combine terms efficiently using properties like the distributive property.

Arithmetic operations are the basic building blocks of mathematics. They include five main types: addition, subtraction, multiplication, division, and exponentiation. These operations allow us to manipulate numbers in various ways to solve problems.

In our exercise, multiplication and addition are the key arithmetic operations. By using them together with the distributive property, we can simplify the task of finding the value of expressions such as \(8(2+9)\). First, we multiply separately, and then we use addition to combine the results. This demonstrates how different arithmetic operations can work together seamlessly.

The sum of products is a method where individual multiplication results are added together. This concept is very useful in algebra and helps in simplifying expressions, such as those found in distributive properties.

When we apply the distributive property, \(8(2+9)\) becomes \(8 \cdot 2 + 8 \cdot 9\). Here, each multiplication—\(8 \cdot 2\) and \(8 \cdot 9\)—is computed separately, giving us products. These products, which are 16 and 72, are then summed up, providing a final total of 88.

This method makes calculations more structured and less prone to error, especially when dealing with complex numbers or expressions. It underscores how addition of individual multiplication results leads to a comprehensive solution.