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When working with algebraic expressions, you'll often encounter terms that contain the same variable raised to the same power. These are known as *like terms*. Identifying these terms is crucial for simplifying expressions. For example, in the expression

• \((7x, -3x, 2x)\),

they are all like terms because they all contain the variable \(x\) raised to the first power. Focusing on like terms allows us to combine them into a single, simpler term.
To simplify, we only need to add or subtract their coefficients (the numbers in front of the variables). This can make the problem less complex and easier to solve.

Alongside like terms, you'll also find constants in expressions. These are numbers without variables. In our example, the constants are:

• 1, 5, and -4

Just like with like terms, you can combine constants by adding or subtracting them. This helps in reducing the complexity of the expression.
After combining, the constants determine the independent part of the simplified expression. In our original exercise, combining the constants results in:

• 1 + 5 - 4 = 2

Thus, the simplified version of the constants contributes the number 2 to the final expression.

Simplifying an algebraic expression involves combining like terms and constants into a more manageable form. The primary aim is to make the expression as neat as possible while retaining its core value. Let's break down the simplification steps:1. **Identify Like Terms**: Look for terms with identical variables and exponents. - In the expression (\(7x, -3x, 2x\)), these were identified as like terms.2. **Combine Like Terms**: Add or subtract their coefficients. - Performing \(7x - 3x + 2x\) gives us \(6x\).3. **Combine Constants**: Add or subtract constants to further simplify. - Adding \(1, 5,\) and \(-4\) results in \(2\).4. **Write the Simplified Expression**: Combine the results from the above steps. - Hence, the simplified form of the initial expression becomes \(6x + 2\).By following these steps, complex expressions can be simplified efficiently, aiding in problem solving and understanding of algebraic manipulation.