Expanding Algebraic Expressions
Expanding an algebraic expression means removing the brackets by multiplying each term inside the bracket by the term outside. This uses the distributive property of multiplication over addition.
For example, 3(x + 4) = 3x + 12. The bracket has been “opened up” by multiplying each term inside by 3.
What is Expanding Algebraic Expressions - Grade 7 Maths (Algebraic Expressions and Identities)?
Definition: Expanding means applying the distributive property to remove brackets from an algebraic expression:
a(b + c) = ab + ac
This also works with subtraction: a(b − c) = ab − ac.
Expanding Algebraic Expressions Formula
Key expansion rules:
- a(b + c) = ab + ac
- a(b − c) = ab − ac
- −a(b + c) = −ab − ac
- −a(b − c) = −ab + ac
Types and Properties
Types of expansion problems:
- Single bracket: 5(2x + 3) = 10x + 15
- Negative outside bracket: −2(x − 4) = −2x + 8
- Variable outside bracket: x(x + 5) = x² + 5x
- Two terms outside: (x + 2)(x + 3) — expand using FOIL or distribution (Class 8+)
Solved Examples
Example 1: Simple Expansion
Problem: Expand 4(x + 7).
Solution:
- 4 × x + 4 × 7 = 4x + 28
Answer: 4x + 28.
Example 2: Expansion with Subtraction
Problem: Expand 3(2y − 5).
Solution:
- 3 × 2y − 3 × 5 = 6y − 15
Answer: 6y − 15.
Example 3: Negative Multiplier
Problem: Expand −2(3a + 4).
Solution:
- (−2) × 3a + (−2) × 4 = −6a − 8
Answer: −6a − 8.
Example 4: Variable Outside Bracket
Problem: Expand x(x + 6).
Solution:
- x × x + x × 6 = x² + 6x
Answer: x² + 6x.
Real-World Applications
Real-world uses:
- Area calculations: Area of a rectangle with sides (x + 3) and 4 = 4(x + 3) = 4x + 12.
- Simplifying expressions: Expanding helps combine and simplify algebraic expressions.
- Solving equations: Many equations require expanding brackets before solving.
Key Points to Remember
- Expanding means removing brackets using the distributive property.
- Multiply every term inside the bracket by the term outside.
- Watch the signs carefully: negative × negative = positive.
- −a(b − c) = −ab + ac (the signs flip).
- After expanding, combine like terms if possible.
Practice Problems
- Expand 5(3x + 2).
- Expand −4(y − 3).
- Expand 2a(a + 5).
- Expand and simplify: 3(x + 4) + 2(x − 1).
Frequently Asked Questions
Q1. What does expanding mean in algebra?
Expanding means removing brackets by multiplying each term inside the bracket by the term outside, using the distributive property: a(b + c) = ab + ac.
Q2. What is the distributive property?
The distributive property states that a(b + c) = ab + ac. Multiplication distributes over addition (and subtraction).
Q3. What happens when a negative number is outside the bracket?
Each term inside the bracket is multiplied by the negative number. The signs change: −2(x + 3) = −2x − 6, and −2(x − 3) = −2x + 6.
