91Ó°ÊÓ

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. Think of it as a way to represent a relationship or a value.

Variables are letters that stand in for unknown numbers. Common variables include x, y, and z. For example, in the expression 8x, 8 is the coefficient, and x is the variable.

Constants are numbers without variables attached. In the expression -3 + 8x + 4, both -3 and 4 are constants.

Expressions can involve addition, subtraction, multiplication, and division. They can be simple, like 5x + 3, or more complex, like the one we’re dealing with: -3 + 8x + 4 + (-10x). Understanding algebraic expressions is key to mastering algebra!

Like terms are terms in an algebraic expression that have identical variable parts. This means that the variables are the same and they are raised to the same power. For example, in the expression 8x + (-10x) + 4 + (-3), the like terms are:
• 8x and -10x (because both terms have the variable x)
• -3 and 4 (because they are both constant terms, without variables)

Non-like terms cannot be combined directly. For instance, 8x cannot be combined with 4 because one is a variable term and the other is a constant. Recognizing and combining like terms is critical for simplifying expressions.

Simplifying expressions involves combining like terms to make the expression as concise as possible. Let’s break down the steps for the expression -3 + 8x + 4 + (-10x):

Step 1: Identify the like terms. Here, -3 and 4 are constants, and 8x and -10x are variable terms.

Step 2: Combine the constant terms: -3 + 4 = 1.

Step 3: Combine the variable terms: 8x + (-10x) = -2x.

Step 4: Write the simplified expression: 1 - 2x.

By following these steps, you can simplify even complex expressions. Remember, stay organized and take one step at a time to avoid confusion. Happy simplifying!