Expanding & Factorising
This topic covers 5 learning steps, guiding your child from the basics through to confident problem-solving. Each step includes a worked example and adaptive practice questions.
What Your Child Will Learn
- Expand single brackets
Expand expressions like 3(x + 4) - Expand double brackets
Expand (x + 2)(x + 3) - Factorise common factors
Factorise 6x + 12 = 6(x + 2) - Factorise quadratics
Factorise x² + 5x + 6 - Difference of two squares
Factorise x² - 9 = (x-3)(x+3)
Common Mistakes
- Forgetting to multiply every term inside the bracket (e.g. expanding 3(x + 4) as 3x + 4 instead of 3x + 12)
The number outside the bracket multiplies EVERY term inside. Think of it as distributing: 3 × x = 3x AND 3 × 4 = 12, so 3(x + 4) = 3x + 12. - Getting the signs wrong when expanding double brackets, especially with negatives (e.g. (x + 3)(x - 2) — missing that 3 × -2 = -6)
Use FOIL (First, Outside, Inside, Last) and be very careful with signs. (x + 3)(x - 2) = x² - 2x + 3x - 6 = x² + x - 6. Check by substituting a number like x = 1: (4)(−1) = −4, and 1 + 1 − 6 = −4.
Tips for Parents
- Think of expanding brackets as "removing the brackets" by multiplying everything inside by what is outside. Use a grid method: draw a 2×2 grid for double brackets.
- Factorising is the reverse of expanding — it puts the brackets back. Ask your child: "What number goes into both 6x and 12? It is 6, so 6x + 12 = 6(x + 2)."
- Practise expanding and factorising as a pair: expand 3(x + 5) = 3x + 15, then factorise 3x + 15 back to 3(x + 5). They should get back to where they started.
- For double brackets, the grid method is very reliable: put one bracket across the top and the other down the side, fill in each cell, then collect like terms.
Key Words
- Expand — Remove brackets by multiplying — 3(x + 4) becomes 3x + 12.
- Factorise — Put brackets back in by finding common factors — 6x + 12 becomes 6(x + 2).
- Common factor — A number or letter that divides evenly into every term — 3 is a common factor of 6x and 12.
- Like terms — Terms with the same letter and power — 3x and 5x are like terms; 3x and 3x² are not.
- FOIL — A method for expanding double brackets: First, Outside, Inside, Last.
Where This Fits
Before this topic: Children should understand basic algebra, substitution, and collecting like terms, and be comfortable with negative numbers.
After this topic: Expanding and factorising leads to solving quadratic equations, algebraic fractions, and completing the square at GCSE.
How MathCraft Teaches This
In MathCraft, Expanding & Factorising is taught through the Algebra & Arithmetic adventure track. Your child follows guided lessons with friendly characters, works through examples step by step, then practises with questions that adapt to their level.
The adaptive engine tracks mastery across all 5 steps, revisiting concepts your child finds tricky and advancing when they're ready. Parents can see detailed progress in the Parent Dashboard.
Practise Expanding & Factorising with MathCraft
Step-by-step lessons, worked examples, and adaptive practice — all wrapped in an adventure game your child will love.
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