Algebraic Expressions

Introduction

In mathematics, algebraic expressions are combinations of numbers, variables, and mathematical operations. They are used to represent relationships and solve equations.

Terms and Coefficients

• Definition: Terms are the parts of an expression that are added or subtracted. Coefficients are the numbers multiplied by variables in a term.
• Example: In the expression $3x + 2y - 5$, the terms are $3x$, $2y$, and $-5$. The coefficients are 3, 2, and -5.

Like and Unlike Terms

• Definition: Like terms have the same variables raised to the same powers. Unlike terms have different variables or different powers.
• Example: In $4x^2 + 2x - 3x^2 + 5$, $4x^2$ and $-3x^2$ are like terms, while $2x$ and $5$ are unlike terms.

Simplifying Expressions

• Definition: To simplify an expression, combine like terms by adding or subtracting coefficients.
• Example: Simplify $2x + 3y - x + 5y$ by combining like terms: $2x - x + 3y + 5y = x + 8y$.

Common Mistakes

• Forgetting to combine like terms when simplifying expressions.
• Misidentifying like terms due to different powers or variables.

Key Points

• Terms are parts of expressions separated by addition or subtraction.
• Coefficients are numbers multiplied by variables.
• Like terms have the same variables raised to the same powers.
• To simplify expressions, combine like terms by adding or subtracting coefficients.

Practice Questions

1. Simplify the expression: $4a - 2b + 3a + 5b$.
2. Identify the like terms in the expression: $2x^2 - 3y + 4x + 7y$.