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Like terms are a crucial part of algebraic expressions. They are terms that have the same variable with the same exponent. For example, in the expression \(-5t + 13s + 8t - 3s\), the like terms are \(-5t\) and \(8t\), and \(+13s\) and \(-3s\). The coefficients (numbers in front of the variables) can be different, but as long as the variables and their exponents match, the terms are considered like terms. Identifying like terms is essential because it allows you to simplify algebraic expressions by combining them. The process of identifying and combining these terms simplifies the expression, making it easier to work with and understand.

Once like terms have been identified, the next step is to combine them. This process involves adding or subtracting the coefficients of the like terms while keeping the variable part unchanged. For example, let's take the expression \(-5t + 8t + 13s - 3s\). We can group the like terms together: \(-5t + 8t \) and \(13s - 3s\). When we add or subtract the coefficients: \[-5 + 8 = 3\] and \[13 - 3 = 10\]. This results in the simplified expression of \3t + 10s.\ By combining like terms, we effectively reduce the expression to its simplest form, thereby making it easier to handle.

Algebraic addition and subtraction are the operations used to simplify expressions by combining like terms. In our example, we were given \(-5t + 13s + 8t - 3s\) and were asked to add or subtract as indicated. Here’s how algebraic addition and subtraction were used to simplify the expression: First, we identified the like terms and grouped them: \(-5t + 8t\) and \(13s - 3s\). Then, we added or subtracted the coefficients of these like terms, resulting in \3t\ and \10s.\ So the simplified expression is \3t + 10s.\ Algebraic addition and subtraction make it much easier to work with expressions by breaking them down into manageable parts. Remember to always look for and combine like terms, keep track of positive and negative signs, and carefully add or subtract coefficients.