An algebraic expression is a mathematical phrase that includes numbers, variables (like x or y), and operations such as addition, subtraction, multiplication, and division. The purpose of an algebraic expression is to represent a relationship or a rule for a certain set of values.

The key parts of an algebraic expression are:

• Terms: These are the parts of the expression that are added or subtracted. For example, in the expression 3x + 5, 3x and 5 are terms.
• Variables: These are symbols (usually letters) that represent unknown values. For example, in the expression 3x + 5, x is the variable.
• Coefficients: These are the numbers that multiply the variables. For example, in the term 3x, 3 is the coefficient of the variable x.
• Constants: These are numbers that stand alone without a variable. For example, in the expression 3x + 5, 5 is the constant.

Examples:

Example 1: Simplifying an Algebraic Expression
Simplify: 2x + 3x
Step 1: Combine like terms (terms that have the same variable, like x).
2x + 3x = 5x
So, the simplified expression is 5x.

Example 2: Evaluating an Algebraic Expression
Evaluate the expression 4x + 7 for x = 3.
Step 1: Substitute the value of x into the expression.
4(3) + 7 = 12 + 7 = 19
So, the value of the expression when x = 3 is 19.

Algebraic expressions are a fundamental concept in algebra. They are used to represent a wide variety of mathematical situations, such as calculating areas, solving equations, and working with patterns.

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