Learning Objectives
- Identify terms, factors, and coefficients of algebraic expressions
- Classify expressions as monomials, binomials, trinomials, and polynomials
- Add and subtract algebraic expressions
- Find the value of an expression for given values of variables
Key Concepts
Parts of an Algebraic Expression
Terms: Parts of an expression separated by + or - signs.
Coefficient: The numerical part of a term (e.g., in 5xy, the coefficient is 5).
Like Terms: Terms with the same variable parts (e.g., 3x and 7x are like terms).
Types of Expressions
- Monomial: One term (e.g., 5x²)
- Binomial: Two terms (e.g., 3x + 4)
- Trinomial: Three terms (e.g., x² + 3x + 2)
- Polynomial: One or more terms with non-negative integer exponents
Addition and Subtraction
Only like terms can be added or subtracted. Combine the coefficients of like terms.
Example: (3x + 5y) + (2x - 3y) = 5x + 2y
Summary
Algebraic expressions use variables, constants, and operations. Terms are classified by their variable parts. Like terms can be combined through addition or subtraction. Expressions can be evaluated by substituting values for variables.
Important Terms
- Variable
- A symbol (usually a letter) that can take different numerical values
- Constant
- A fixed numerical value in an expression
- Coefficient
- The numerical factor of a term
- Like Terms
- Terms with identical variable parts
Quick Revision
- Like terms have the same variables with the same exponents
- Only like terms can be added or subtracted
- Coefficient of x in 5x is 5; coefficient of x in -x is -1
- A monomial has 1 term, binomial has 2, trinomial has 3
- To evaluate: substitute the given values and calculate
Practice Tips
- Identify like terms before performing addition/subtraction
- Use tables to organize terms when adding or subtracting expressions
- Practise evaluating expressions with different values of variables