Addition of Algebraic Expressions
Adding algebraic expressions means combining like terms. Like terms have the same variable parts — you add their coefficients. Unlike terms are written as they are.
There are two methods: horizontal method (write expressions side by side) and column method (write like terms in columns and add vertically).
What is Addition of Algebraic Expressions - Grade 7 Maths (Algebraic Expressions)?
Rule: To add algebraic expressions, combine like terms by adding their coefficients. Unlike terms remain unchanged.
Like terms: Same variables with same powers. 3x² and 5x² → like. 3x and 5x² → unlike.
Addition of Algebraic Expressions Formula
Add coefficients of like terms. Write unlike terms as is.
Types and Properties
Methods:
- Horizontal method: Write both expressions, group like terms, add coefficients.
- Column method: Write like terms in columns, add each column.
Solved Examples
Example 1: Adding Two Binomials
Problem: Add: (3x + 5) + (2x + 7)
Solution:
- Like terms: 3x + 2x = 5x
- Constants: 5 + 7 = 12
Answer: 5x + 12.
Example 2: Adding Trinomials
Problem: Add: (x² + 3x + 2) + (2x² − x + 5)
Solution:
- x² + 2x² = 3x²
- 3x + (−x) = 2x
- 2 + 5 = 7
Answer: 3x² + 2x + 7.
Example 3: Column Method
Problem: Add: (4a² − 3ab + b²) + (2a² + 5ab − 3b²)
Solution (column):
- a² terms: 4a² + 2a² = 6a²
- ab terms: −3ab + 5ab = 2ab
- b² terms: b² + (−3b²) = −2b²
Answer: 6a² + 2ab − 2b².
Example 4: Adding Three Expressions
Problem: Add: (2x + 3) + (x − 4) + (5x + 1)
Solution:
- x terms: 2x + x + 5x = 8x
- Constants: 3 + (−4) + 1 = 0
Answer: 8x.
Real-World Applications
Real-world uses:
- Combining costs: If cost of item A is (2x + 5) and item B is (3x + 2), total cost = 5x + 7.
- Perimeter: Adding side expressions gives total perimeter as an algebraic expression.
Key Points to Remember
- Only like terms can be added.
- Add the coefficients; keep the variable part the same.
- Unlike terms are written as they are.
- Use horizontal or column method — both give the same result.
Practice Problems
- Add: (4x + 3) + (x − 2)
- Add: (2a² + a − 1) + (a² − 3a + 4)
- Add: (3p + 2q) + (p − q) + (2p + 3q)
- Add: (x² + xy + y²) + (2x² − xy + 3y²)
Frequently Asked Questions
Q1. How do you add algebraic expressions?
Identify like terms (same variable parts) and add their coefficients. Write unlike terms as they are.
Q2. Can unlike terms be added?
No. Unlike terms cannot be combined. 3x + 2y stays as 3x + 2y.
Q3. Is addition of expressions commutative?
Yes. (A + B) gives the same result as (B + A).
