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Combining like terms is a simple yet essential skill in algebra. It involves adding or subtracting terms that have the same variables and exponents.
This concept helps in simplifying algebraic expressions, making them easier to work with.
In the given exercise, the expression is: \(43m + (-12n) + (-16m) + (-9n)\).
To simplify it, we first identify terms with the same variable:

• 43m and -16m are like terms because they both have the variable \(m\).
• -12n and -9n are like terms because they both have the variable \(n\).

Next, we combine these like terms:

• \(43m - 16m = 27m\)
• \(-12n - 9n = -21n\)

Finally, we write the simplified expression: \(27m + (-21n)\). Understanding how to combine like terms effectively will not only simplify your expressions but also make solving equations much easier.

Variables are symbols, typically letters like \(m\) or \(n\), used to represent unknown values in algebraic expressions and equations.
They are fundamental to prealgebra and algebra because they allow us to generalize mathematical statements and solve problems involving unknown quantities.
In the exercise, the variables are \(m\) and \(n\), each associated with different coefficients.
When you see an expression like \(43m\), it means 43 times an unknown value represented by \(m\).
Variables can also change depending on the problem at hand, making them versatile tools for different mathematical scenarios.
When solving problems, always keep track of your variables and ensure you are combining only the terms with the same variable for accurate simplification.

Prealgebra lays the foundation for all higher-level math courses, involving basic operations and simple algebraic tasks.
It introduces students to the basic concepts of algebra, simplifying expressions, and solving equations.
Skills like combining like terms and understanding variables are crucial at this level.
The given problem, \(43m + (-12n) + (-16m) + (-9n)\), involves key prealgebra skills.
First, we identify like terms, then combine them by performing basic arithmetic operations.
Mastering prealgebra concepts ensures a strong mathematical foundation, making future algebra topics less daunting and more intuitive.
Practicing these skills regularly will make transitioning to more complex algebra topics smoother.