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Algebraic expressions often contain terms that look similar. These are called **like terms**. They have exactly the same variables raised to the same powers. It means if you have terms like \(3rst\), \(4rst\), and \(7rst\), they are all like terms because each contains the same combination of the variables \(r\), \(s\), and \(t\). Understanding which terms are alike is the first step in simplifying expressions.
To identify like terms, focus on the variables and their exponents. If both are identical in two or more terms, you can group these terms together. This step is crucial for simplifying any algebraic expression efficiently. It helps in avoiding mistakes and makes arithmetic operations straightforward.

In algebra, numbers come before variables in terms. These numbers are known as **coefficients**. Coefficients tell us how many times we need to take the variable they’re attached to. For an example, in \(3rst\), the number \(3\) is the coefficient of \(rst\).
Recognizing coefficients is vital because it helps you perform operations like addition or subtraction of terms. When you have like terms, you only add or subtract the coefficients while the variables remain unchanged. This makes it much easier to manage and simplify expressions.

Once you have identified like terms and their coefficients, you can easily perform the **addition of terms**. Here's how it works:

• Identify the like terms in your expression.
• Add their coefficients together. In our example, adding \(3 + 4 + 7\) gives \(14\).
• Keep the variable part (e.g., \(rst\)) unchanged.

By following this approach, the arithmetic becomes simple because you only add the numbers in front of the variables. The final expression for our original problem becomes \(14rst\). This process not only simplifies the expression but reduces possible confusion when handling multiple terms.