Terms of an Algebraic Expression
An algebraic expression is made up of terms. Each term is a product of numbers and variables. For example, in 3x² + 5x − 7, the terms are 3x², 5x, and −7.
Understanding terms is the first step to working with algebraic expressions — you need to identify terms before you can add, subtract, or simplify expressions.
What is Terms of an Algebraic Expression - Grade 7 Maths (Algebraic Expressions)?
Definition: A term is a single part of an algebraic expression, separated by + or − signs.
Parts of a term:
- Coefficient: The numerical part. In 5x², the coefficient is 5.
- Variable: The letter(s). In 5x², the variable part is x².
- Constant term: A term with no variable. Example: −7.
Like terms: Terms with the same variable parts. Example: 3x and 5x are like terms. 3x and 3x² are NOT like terms.
Terms of an Algebraic Expression Formula
Expression = Term₁ + Term₂ + Term₃ + ...
Types and Properties
Types of Terms:
- Constant term: Just a number, no variable. Example: 5, −3.
- Variable term: Contains a variable. Example: 3x, −2y².
- Like terms: Same variable part. Example: 4x and −2x.
- Unlike terms: Different variable parts. Example: 3x and 3y.
Solved Examples
Example 1: Identifying Terms
Problem: List the terms of: 4x² − 3x + 7
Solution:
- Term 1: 4x²
- Term 2: −3x
- Term 3: 7
Answer: Three terms: 4x², −3x, 7.
Example 2: Coefficients
Problem: Find the coefficient of each term in 5xy − 2y + 1.
Solution:
- 5xy → coefficient = 5
- −2y → coefficient = −2
- 1 → constant (coefficient concept doesn't apply to constants, or you can say coefficient = 1 with no variable)
Answer: Coefficients: 5, −2. Constant: 1.
Example 3: Like and Unlike Terms
Problem: Identify like terms: 3x, 5y, −2x, 7, 4y
Solution:
- 3x and −2x are like terms (both have x).
- 5y and 4y are like terms (both have y).
- 7 is a constant.
Answer: Like terms: {3x, −2x} and {5y, 4y}.
Real-World Applications
Why this matters:
- Identifying terms is needed for simplification of expressions.
- Like terms can be combined; unlike terms cannot.
- Understanding coefficients helps in solving equations.
Key Points to Remember
- Terms are separated by + or − signs.
- The coefficient is the numerical factor of a term.
- A constant is a term without a variable.
- Like terms have the same variable parts (same variables raised to same powers).
- Only like terms can be combined (added or subtracted).
Practice Problems
- List the terms of 2a² + 3ab − 4b + 5.
- Find the coefficient of y in −7xy.
- Identify like terms: 4p², −3p, 2p², 5q, −p.
- How many terms does 3x − y + z − 2 have?
Frequently Asked Questions
Q1. What is a term in algebra?
A term is a single part of an expression, consisting of a number (coefficient) multiplied by variables. Terms are separated by + or − signs.
Q2. What are like terms?
Terms with exactly the same variable parts. For example, 3x² and −5x² are like terms. But 3x² and 3x are NOT like terms.
Q3. Can a constant be a term?
Yes. A constant like 7 or −3 is a term with no variable part. It is called a constant term.
