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The distributive property is a fundamental concept in algebra that lets you simplify expressions and solve equations more easily. It states that multiplying a single term across a sum or difference inside parentheses is the same as doing the multiplication separately and then adding or subtracting the results.
When you see an expression like \(a(b + c)\), you can distribute \(a\) to both \(b\) and \(c\), which gives you \(ab + ac\). This is particularly useful when simplifying algebraic expressions because it allows you to eliminate brackets.
In our example, \(5n-(7-2n)\), you treat the negative sign in front of the bracket as multiplying by \(-1\). Then use the distributive property to get \(5n - 7 + 2n\). This step is crucial as it sets you up to simplify the expression further by handling like terms.

Like terms are terms in an expression that have the exact same variable components raised to the same power. Only the coefficients, or numerical parts of these terms, may differ. Being able to identify and combine like terms is important because it helps to simplify expressions into a cleaner form and solve equations faster.
Consider the expression \(5n + 2n\). Both terms are "like" because they both contain the variable \(n\) with the same exponent, which is 1 by default. You simply add together the coefficients (the numbers in front of the variables), to get \(7n\).
Understanding like terms allows you to clean up expressions. For example, in \(5n - 7 + 2n\), \(5n\) and \(2n\) are like terms. Combine them as such: \(5 + 2 = 7\), resulting in the term \(7n\). The \(-7\) is a constant and remains separate.

Algebraic expressions are combinations of variables, numbers, and operations such as addition, subtraction, multiplication, and division. They are used to represent mathematical relationships in a more general way than merely using specific numbers.
Expressions can vary in complexity from simple to very complex, incorporating multiple variables and operations. These expressions can be evaluated or simplified by applying various algebraic rules and properties such as the distributive property and combining like terms.
In our task, we initially have the expression \(5n-(7-2n)\). Our goal is to simplify it by eliminating parenthesis using the distributive property and then combining the like terms to make it as simple and tidy as possible. The end result is a much simpler expression \(7n - 7\).
Learning how to work with algebraic expressions is essential for solving more complex equations and understanding mathematical models in algebra and beyond.