GCSE · Maths · AQA · Spec 8300 · Foundation
Expanding single brackets
The term outside a bracket has one job: multiply every term inside. The classic slips are a term it skipped or a sign it forgot.
Algebra · Expanding brackets
Which of these really are the bracket, multiplied out?
Each line claims to expand a bracket. Pick one, then put it where it belongs: is it right, or what went wrong?
Still to sort
Correct (0)
Every term inside got its own multiplication, sign and power right.
Where the line is: Check the count: one product for each term in the bracket. If any is missing or off, it lives in another column.
A term got missed (0)
Some of the inside was never multiplied.
Where the line is: If every term was multiplied but a sign came out wrong, it belongs in the sign column instead.
A sign went wrong (0)
The numbers look fine, but a + or − is wrong.
Where the line is: A negative outside multiplies every term inside, so every sign inside changes, not just the first.
The powers went wrong (0)
The x's have been multiplied, but not correctly.
Where the line is: Multiplying adds the powers: x × x = x² and x² × x³ = x⁵. Multiplying the powers, or writing x × x as 2x, lands here.
Predict, then check
Same symbols. One pair of brackets. Does it matter?
Take x = 4. Do 3(x + 2) and 3x + 2 give the same value?
Two brackets at once
Problem
Expand and simplify: (a) 3(2x + 5) + 2(x − 4) (b) 4(3x + 2) − 2(x − 5) (c) 3(x + 2) + 5(x + 2)
WHAT YOU'VE LEARNED
A quick recap of today's lesson.
Some of the expansions below are right and some are quietly wrong. One rule decides which. See if you can find it.
What you need to know
- The term outside a bracket multiplies every term inside it, not just the first.
- A negative outside the bracket changes the sign of every term inside.
- Multiplying powers of the same letter adds the powers: x² × x³ = x⁵.
- After expanding, collect like terms. Give the simplest form even when the question doesn't say 'simplify'.
The big picture
Expanding a bracket means multiplying it out. Whatever sits outside, whether a number, a negative, a fraction or a term like x², multiplies every term inside, signs included: −3(2x − 5) = −6x + 15, and x²(x³ + 4x) = x⁵ + 4x³, since multiplying powers of the same letter adds them. With two brackets, expand each, then collect like terms into the simplest form. A minus in front of a bracket belongs to the number after it. Check any expansion by substituting a number into both versions.
Key points
Worked example
Problem
Expand and simplify x(x + 6) + ½(6x² − 4x).
⚠ Watch out
Changing only the first sign when the outside term is negative. −5(x − 2) = −5x − 10 is wrong: the −5 multiplies the −2 as well, and −5 × −2 = +10. So −5(x − 2) = −5x + 10.
Memory hook
Knock on every door. The term outside the bracket visits every term inside, and a minus sign goes with it on every visit.
Check yourself
Expand and simplify 5(x − 1) − 2(3 − x). (Answer: 7x − 11, since −2 × 3 = −6 and −2 × −x = +2x.)
Flashcards
(12)What does 3(x + 5) mean?
What is the distributive law?
Expand −2(x − 4).
What is −(x − 7)?
What is x² × x³?
Someone writes x × x = 2x. What's wrong?
Expand ½(8x − 6).
Expand 3a(2a + b).
How do you deal with the minus in 5(x + 1) − 2(x − 3)?
Which of these are like terms: 3x, 3x², 5x?
How can 4(x + 3) + 2(x + 3) be done in one step?
How can you check an expansion?
Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.
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