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Simplifying mathematical expressions makes them easier to work with. When dealing with complex expressions, breaking them down into simpler parts is essential. In this exercise, we used the distributive property to simplify an expression. The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products. The form looks like this: a(b + c) = ab + ac For our example, we applied this property: First, take the expression: \[ 7(3n + 9) - (4n -13) \]We distribute 7: \[ 7(3n) + 7(9) = 21n + 63 \]Then, distribute the minus sign to the next term:\[ -(4n - 13) = -4n + 13 \]Simplifying expressions involves more than just distributing; knowing when and how to apply properties like the distributive property will make this task simpler.

Combining like terms is crucial for simplifying expressions fully. Like terms are terms that have identical variable parts. In our case, we used it after applying the distributive property and simplifying different parts of the expression individually. For example, the expression after distribution was:\[ 21n + 63 - 4n + 13 \]Notice that 21n and -4n are like terms because they both have the variable 'n'. Combining them gives us:\[ 21n - 4n = 17n \]Similarly, the constants 63 and 13 can be combined:\[ 63 + 13 = 76 \]Putting it all together, we get:\[ 17n + 76 \]This simplification is essential because a sum of terms similar in form can drastically reduce the complexity of an expression.

Prealgebra is foundational for further study in algebra and beyond. It provides tools and techniques to manipulate and simplify expressions. Understanding basic algebra concepts, such as the distributive property and combining like terms, is crucial. In dealing with the expression \( 7(3n+9)-(4n-13) \), we employed prealgebra techniques. Here are some vital techniques used:

• Distributive Property: Simplifies expressions by distributing multiplication over addition or subtraction. Understanding this is essential for simplifying and breaking down expressions.
• Combining Like Terms: Simplifying by adding or subtracting terms that contain the same variables or constants.
• Basic Arithmetic Operations: Addition, subtraction, multiplication, and understanding of negation are fundamental steps in dealing with more complex algebraic expressions.

These techniques form the basis not only for algebra but also for understanding and succeeding in various fields of mathematics. Building a solid foundation in prealgebra ensures students are well-prepared for more advanced mathematical challenges.