Y9-L03 · Simplifying & Expanding 20 09 2026
Simplifying & Expanding
Combine like terms, multiply into brackets, and tidy the result.
By the end, you can…
- identify like terms and collect their coefficients;
- expand one bracket, including a negative multiplier;
- expand two separate brackets and then simplify;
- check an identity by substituting a number.
Recall
Coefficient means the number multiplying a letter. In −4x, the coefficient is −4.
Like terms have exactly the same letters and powers: 3x and −7x are like terms; 3x and 3x² are not.
Collect like terms
= (7x − 2x) + (3y + 5y)
= 5x + 8y
Group terms with identical letter parts. Add or subtract only their coefficients.
Multiply every term
= (−3 × 2x) + (−3 × −5)
= −6x + 15
A negative times a negative is positive. Include the sign when multiplying.
Two brackets, one tidy result
= 4x + 8 − 3x + 15
= x + 23
The second bracket is multiplied by −3, so −3 × −5 gives +15.
Quick check: put x = 2 into 4(x + 2) − 3(x − 5): 16 + 9 = 25. Put x = 2 into x + 23: 25. Both forms agree.
Practise the skill
Work it out before choosing an answer. The questions progress from collecting terms to longer expansions.
Algebra Words, Terms and Expansion
5 matching questions + 20 multiple-choice questions · 25 marks
Instructions: Match the definitions in Part A. Choose one answer for each question in Parts B–D. Work through the algebra on paper before choosing. Each question is worth 1 mark. Submit to see your score and explanations.
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