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Understanding algebraic expressions is crucial for mastering algebra. An algebraic expression is a combination of numbers, variables, and operations. In algebraic expressions, variables represent unknown values and are usually denoted by letters such as x, y, s, t, etc. These variables can be raised to different powers and can be multiplied or added with each other.
For example, in the expression \(3s^2 t + r^2 t - 4st^2 - s^2 t + 3st^2 - 7r^2 t\), multiple variables and powers are involved. By mastering algebraic expressions, you gain the ability to manipulate and simplify these expressions effectively.

Like terms are terms within an algebraic expression that have exactly the same variables raised to the same powers. Identifying like terms is essential when you’re simplifying expressions.
In the original exercise, the terms \(3s^2 t\) and \(-s^2 t\) are like terms because both have the variables \(s^2 t\). Similarly, \(-4st^2\) and \(3st^2\) are like terms. Recognizing these allows you to group and then combine them.
The key to finding like terms lies in ensuring that the variable parts must match exactly. Different coefficients (the numbers in front of the variables) don't matter when identifying like terms.

Simplifying expressions involves combining like terms to reduce the expression to its simplest form. Here's how you can do it in a step-by-step manner:
1. Identify like terms: This is the first step, where you scan the expression to find terms with the same variable parts.
2. Group like terms together: Rearrange the expression to place all like terms next to each other. In the example, it groups into \(3s^2 t - s^2 t\), \(r^2 t - 7r^2 t\) and \(-4st^2 + 3st^2\).
3. Combine the coefficients: For each group, add or subtract the coefficients while keeping the variables part unchanged.
4. Rewrite the simplified expression: After combining, you write down the new simplified expression. For the provided example, combining results in \(2s^2 t - 6r^2 t - st^2\).
By following these steps rigorously, you'll master the skill of simplifying complex algebraic expressions efficiently.