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The distributive property allows us to multiply a sum by distributing the multiplication over each addend inside the parentheses. This way, we make multiplication easier and more manageable. In our expression, we start with the term 8 and the sum inside the parentheses \(m+3\).
To use the distributive property, we multiply 8 by each term inside:

• Multiply 8 by \(m\), resulting in \(8m\)
• Multiply 8 by 3, resulting in 24

Putting these two results together, the expression within the parentheses \(m+3\) becomes \(8m + 24\).
This step breaks down the problem, so it's easier to handle individual components before moving on to the next part.

Combining like terms is a technique used to simplify algebraic expressions. This technique involves merging terms that have the same variables raised to the same power.
In our example, after applying the distributive property, the expression is \(8m + 24 - 20 + m\).
Here, we have the following like terms:

• Terms with \(m\): \(8m\) and \(m\), which add up to \(9m\)
• Constant terms: 24 and -20, which add up to 4

By combining the like terms, the expression is simplified to \(9m + 4\).
This simplification step reduces complexity and ensures that similar elements in the expression are represented together.

Prealgebra lays the groundwork for understanding algebra by introducing basic mathematical concepts. It focuses on foundational arithmetic and simple algebraic concepts, making it accessible and manageable for beginners.
In expressions like the one we provided, prealgebra helps students develop skills in:

• Understanding how to manipulate equations using basic arithmetic operations
• Learning properties like the distributive property to simplify calculations
• Recognizing and combining like terms to streamline problem solving

As learners apply these prealgebra strategies, they establish a solid base to move forward with more complex algebraic concepts. By mastering these core principles, students gain confidence in tackling mathematical problems efficiently. This journey through prealgebra is often characterized by learning how to break down and simplify expressions just like the one in our example.