Why This Lesson Matters
Turn a complicated-looking equation into a clear sequence of steps.
Equations with brackets appear in IGCSE maths. Once you understand how to expand correctly, these equations become much more structured and manageable.
This topic also prepares you for factorising, quadratics, algebraic manipulation and more advanced algebra.
What You Will Learn
Open the cards to view the skills you will develop.
- Expand and simplify expressions with positive and negative multipliers.
- Solve equations with x on both sides, including negative and fractional solutions.
- Form an equation from a geometric situation and interpret the answer.
- Extended: clear numerical denominators, retaining brackets and signs.
What do you already know?
Three quick questions will wake up the skills you need. This is not a test — just have a go.
Brackets mean multiplication
When equations include brackets, they may look more difficult, but the process is still simple. The key is to carefully expand the brackets, then solve step by step.
To remove brackets, multiply everything inside the bracket by the number outside. This is the .
See what the 3 multiplies
Press play to watch the brackets expand step by step with narration.
Start with three groups of (x + 4).
Recorded narration. Select Play to begin; use the speed control for a slower explanation.
Read the full narration
Three multiplies everything inside the brackets. This means three groups of x plus four.
First, three times x gives three x.
Then, three times four gives twelve.
Add the two products. Three times the quantity x plus four equals three x plus twelve. Remember to multiply every term inside the brackets.
(x + 4) + (x + 4) + (x + 4) = 3x + 12. There are three x terms and twelve units.
The brackets hold one whole group. Multiplying by 3 makes three copies of everything in that group.
So 3(x + 4) = 3x + 12. Writing 3x + 4 would copy x three times but include the four only once.
The term outside the brackets stays outside
In 7 − 2(3x − 4), the multiplier of the bracket is −2. The 7 is a separate term.
Now collect the constants: 7 − 6x + 8 = 15 − 6x.
Subtracting 2(3x − 4) is the same as adding −2 times the whole bracket. That gives −6x + 8.
The 7 is not inside the bracket and is not multiplied. Brackets specify the scope of an operation.
Simplify 7 − 2(3x − 4).
Choose one answer.
Keep the sign with its term
Distribute the number outside the brackets to each term inside. Apply the multiplication sign rules to each product.
2(x + 5)
2 × x and 2 × 5
2x + 104(2x − 3)
4 × 2x and 4 × (−3)
8x − 12−2(x − 6)
−2 × x and −2 × (−6)
−2x + 12−3(2x + 7)
−3 × 2x and −3 × 7
−6x − 21Remember: positive × negative is negative; negative × negative is positive. Then collect any like terms.
Look at −2(x − 6). Subtracting 6 changes the group by −6; multiplying that change by −2 gives +12.
You can check with x = 6: the original is −2(6 − 6) = 0, and −2 × 6 + 12 = 0. The incorrect expression −2x − 12 would give −24.
Connect each bracket to its equivalent expression
Drag and drop each expression into its matching expansion. Or select a card, then select its destination using touch or keyboard.
One group. Every part.
Repeated structures help us see equal groups. In algebra, 3(x + 4) means three copies of the whole group—not three copies of x alone.
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