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When we talk about simplifying expressions, we're referring to the process of making a mathematical expression easier to work with. This usually involves reducing the number of terms and combining those that are similar. For example, in the exercise given, the original expression is \(4y - 1 - (y - 2)\). The first step to simplify this is to distribute the negative sign. This means you apply the sign outside the parentheses to each term inside them. Then, you rewrite the expression in a linear form, getting rid of parentheses or complex groupings. By doing this, you can clearly see the terms that need combining. Simplifying expressions helps us solve equations faster and more efficiently.
Breaking down complex expressions into more manageable parts makes it simpler for students to handle mathematical problems, from prealgebra to more advanced topics.

Combining like terms is a fundamental step in algebra where we merge terms that have the same variable part. In simple words, like terms are terms that have identical variables raised to the same power. For instance, in our exercise after distributing, we end up with \(4y - 1 - y + 2\). We can identify terms with 'y' and terms with numbers separately. Here, \(4y\) and \(-y\) are like terms, so we combine them to get \(3y\). Similarly, \(-1\) and \(+2\) are constants, so we add them together to get \(1\). This leaves us with a simplified expression: \(3y + 1\). Combining like terms is crucial for solving equations and understanding the structure of algebraic expressions.
Doing this reduces the complexity of the equation or expression you are working with and makes further manipulation much easier.

Prealgebra serves as the foundation for all future study in mathematics. It includes basic arithmetic like addition, subtraction, multiplication, and division involving numbers, variables, and a mix of both. The exercise we are looking at involves basic prealgebraic concepts like the distributive property and combining like terms. For instance, understanding how to distribute a negative sign through an expression \(-(y - 2) = -y + 2)\) is an essential prealgebra skill. By mastering these basics, students can confidently move on to more advanced topics in algebra and beyond.
Prealgebra builds a bridge from arithmetic to the broader concepts of algebra, ensuring students have a solid grasp of essential math skills that they'll use throughout their education.