Simplifying algebraic expressions means collecting like terms and reducing expressions to their simplest form. This foundational skill is needed throughout GCSE Maths.
Core Concepts
Collecting Like Terms
Like terms have the same variable(s) raised to the same power.
(xy terms are like terms)
Multiplying Terms
Multiply coefficients and add powers:
Expanding Single Brackets
(careful with the negative!)
Expanding Double Brackets
Use FOIL: First, Outer, Inner, Last.
Dividing Terms
Worked Example: Example 1
Problem
Simplify
Solution
Worked Example: Example 2
Problem
Expand
Solution
Worked Example: Example 3
Problem
Simplify
Solution
Common Mistakes
- Adding unlike terms. .
- Sign errors when expanding brackets. , not .
- Forgetting to multiply all terms inside the bracket.
Practice Problems
- Simplify .
- Expand .
- Expand and simplify .
- Simplify .
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Key Takeaways
Like terms have the same variables and powers.
Expanding: multiply every term inside by every term outside.
FOIL for double brackets.
Watch out for negative signs when expanding.