Subtraction of Algebraic Expressions
Subtracting algebraic expressions means changing the signs of all terms in the expression being subtracted, then adding.
In other words: (A) − (B) = A + (−B). Change every + to − and every − to + in expression B, then add.
What is Subtraction of Algebraic Expressions - Grade 7 Maths (Algebraic Expressions)?
Rule: To subtract expression B from expression A:
- Change the sign of every term in B.
- Add the result to A.
Subtraction of Algebraic Expressions Formula
A − B = A + (−B)
Change signs of all terms in B, then add.
Types and Properties
Common mistake: Only changing the sign of the first term. You must change the sign of EVERY term in the expression being subtracted.
Solved Examples
Example 1: Subtracting Binomials
Problem: Subtract (2x + 3) from (5x + 7).
Solution:
- (5x + 7) − (2x + 3)
- = 5x + 7 − 2x − 3
- = (5x − 2x) + (7 − 3)
- = 3x + 4
Answer: 3x + 4.
Example 2: Subtracting Trinomials
Problem: Subtract (x² − 3x + 2) from (3x² + x − 5).
Solution:
- (3x² + x − 5) − (x² − 3x + 2)
- = 3x² + x − 5 − x² + 3x − 2
- = 2x² + 4x − 7
Answer: 2x² + 4x − 7.
Example 3: With Negative Terms
Problem: Subtract (−2a + 5b) from (3a − 2b).
Solution:
- (3a − 2b) − (−2a + 5b)
- = 3a − 2b + 2a − 5b
- = 5a − 7b
Answer: 5a − 7b.
Real-World Applications
Real-world uses:
- Profit: Revenue − Cost. If revenue = (5x + 100) and cost = (3x + 60), profit = 2x + 40.
- Change: Finding the difference between two measurements expressed algebraically.
Key Points to Remember
- Change the sign of every term in the expression being subtracted.
- Then add the expressions.
- Subtraction is NOT commutative: A − B ≠ B − A.
- "Subtract B from A" means compute A − B (not B − A).
Practice Problems
- Subtract (3x − 2) from (7x + 5).
- Subtract (a² + 2a − 1) from (3a² − a + 4).
- Subtract (−4p + q) from (p − 3q).
- Subtract (2x² − 3x + 1) from (2x² − 3x + 1). What do you get?
Frequently Asked Questions
Q1. How do you subtract algebraic expressions?
Change the sign of every term in the expression being subtracted, then add. (A) − (B) = A + (−B).
Q2. What does 'subtract B from A' mean?
It means calculate A − B. The expression that comes after 'from' is written first.
Q3. Is subtraction commutative?
No. A − B ≠ B − A in general. The order matters.
