Chapter 4: Expressions: expand, collect and factorise
Algebra becomes manageable when you recognise structure rather than treating every symbol separately.
Part of your national curriculum
- Algebra: Use and interpret algebraic notation, including coefficients written as fractions and brackets
- Algebra: Simplify and manipulate algebraic expressions by collecting like terms, multiplying a single term over a bracket and factorising into a single bracket
Lesson overview
What you'll learn in this lesson
Simplify and manipulate algebraic expressions by collecting like terms, multiplying a single term over a bracket and factorising into a single bracket
Key learning points
- • Collect like terms
- • Expand
- • Factorise
This lesson at a glance
- 32 minutes
- 16 parts to scroll through
- 3 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 16
Visual introductionPicture this
Chapter 4: Expressions: expand, collect and factorise
Algebra becomes manageable when you recognise structure rather than treating every symbol separately.
In a nutshell
Simplify and manipulate algebraic expressions by collecting like terms, multiplying a single term over a bracket and factorising into a single bracket
Learning cycle
Part 2 of 16
Learning cycle 1 of 2
Part 1 · Collect like terms
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 16
Learn
Collect like terms
Terms can combine only when their variable parts match: 5x + 2x − 3 = 7x − 3, but x and x² are not like terms.
Reset break
Part 4 of 16
Pause
That's sitting 1 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Explore the idea
Part 5 of 16
Learn
Expand
Multiply the term outside a bracket by every term inside: 3(2x − 5) = 6x − 15. A quick substitution can check equivalence.
Quick check
Part 6 of 16
Quick check
Part 7 of 16
Reset break
Part 8 of 16
Pause
That's sitting 2 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Learning cycle
Part 9 of 16
Learning cycle 2 of 2
Part 2 · Factorise
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 16
Learn
Factorise
Factorising reverses expansion. The highest common factor of 8x + 12 is 4, so 8x + 12 = 4(2x + 3).
Quick check
Part 11 of 16
Reset break
Part 12 of 16
Pause
That's sitting 3 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Challenge round
Part 13 of 16
Game · Sort it
Which of these are true?
Drag each card into the right column. Tap a card first if dragging is fiddly.
True
Not true
Challenge round
Part 14 of 16
Game · Recall cards
Simplify 5a + 3b − 2a + b.
Card 1 of 4
Mastery quiz
Part 15 of 16
Marked quiz
End of lesson quiz: Chapter 4: Expressions: expand, collect and factorise
4 questions, marked with the reasoning shown. No timer.
1. Simplify 5a + 3b − 2a + b.
2. Solve 4x − 7 = 21.
3. Simplify 5x+2x−3.
4. Expand 3(2x−5).
Lesson round-up
Part 16 of 16
Lesson round-up
Ready when you are
Quiz score
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Games
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Points this lesson
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Best run
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Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?
Ask LunaPart 1 of 16 · Watch & discover
How this is going
- Not looked at yet
Use and interpret algebraic notation, including coefficients written as fractions and brackets
- Not looked at yet
Simplify and manipulate algebraic expressions by collecting like terms, multiplying a single term over a bracket and factorising into a single bracket