Expanding brackets and factorising into brackets are a huge part of GCSE Maths. On foundation papers, a whopping 20% of the mark is awarded for algebra and expanding and factorising questions are a large part of that.
So, we know it’s important but how do we know where to start with revision? Our diagnostic tests can help you with just that. Use the expanding and factorising questions below to find gaps in your knowledge. The quiz will tell you exactly what you need to cover in your revision from this list of topics:
– Expanding single brackets
– Expanding and simplifying single brackets
– Expanding double brackets
– Factorising into single brackets
– Factorising quadratics
– The difference of two squares
Expanding and Factorising Diagnostic Test
Results
It looks like you need a bit more practice. Why not take a look at our Expanding and Factorising Revision Bundle to revise the topics you struggled with?
Foundation Expanding and Factorising Digital Revision Bundle
#1. Expand 3(5π₯ + 2).
Topic: Expanding Single Brackets
Check you’ve multiplied every term in the bracket by the term on the outside.
#2. Expand 2π(7π β 5).
Topic: Expanding Single Brackets
Remember, π Γ π = πΒ².
#3. Fully factorise 12π¦ β 6.
Topic: Factorising into Single Brackets
Make sure you take out the largest factor – that’s 6 in this case.
#4. Fully factorise 8π₯Β² β 20π₯.
Topic: Factorising into Single Brackets
Fully factorise means take out the largest possible factor. In this case, that’s 4π₯.
#5. Simplify
3(5π₯ + 7) + 4(2π₯ β 5).
Topic: Expanding and Simplifying Single Brackets
After expanding both brackets, you should get 15π₯ οΌΒ 21 οΌΒ 8π₯ β 20. Then, you just collect the like terms.
#6. Simplify
7(2π₯ β 3) β 2(3π₯ β 1).
Topic: Expanding and Simplifying Single Brackets
Be careful with negatives!Β After expanding both brackets, you should get 14π₯ β 21 β 6π₯ οΌ 2.
#7. Which one of the following expressions is equivalent to
3(2π₯ + 5) β 6(3π₯ β 1)?
Topic: Expanding and Simplifying Single Brackets
Expanding the brackets gives 6π₯ οΌ 15 β 18π₯ οΌ 6. Next, you need to simplify and factorise.Β
#8. Expand (π₯ + 5)(π₯ β 3).
Topic: Expanding Double Brackets
Be systematic when expanding. Make sure you multiply each term in the first bracket by each term in the second. The expanded form before simplifying is π₯2 οΌ 5π₯ β 3π₯ β 15.
#9. Expand and simplify
(3π₯ β 5)Β².
Topic: Expanding Double Brackets
Remember, a bracket squared means multiplied by itself;
(3π₯Β β 5)2 = (3π₯Β β 5)(3π₯Β β 5)
#10. Fully factorise π₯Β² β 5π₯ β 14.
Topic: Factorising Quadratics (π = 1)
You’re looking for a pair of numbers that multiply together to give -14 and add together to give -5.
#11. Expand and simplify:
(π₯ β 7)(π₯ + 7).
Topic: The Difference of Two Squares
Remember, you need to multiply every term in the first bracket by every term in the second bracket.
#12. Expand and simplify
(2π₯ + 3)(5π₯ β 1).
Topic: Expanding Double Brackets
Remember, you need to multiply every term in the first bracket by every term in the second bracket. You should getΒ four terms before simplifying.
#13. Fully factorise π₯Β² β 11π₯ + 18.
Topic: Factorising Quadratics (π = 1)
You’re looking for a pair of numbers that multiply together to give 18 and add together to give -11.
#14. Fully factorise π₯Β² + 7π₯ + 10.
Topic: Factorising into Double Brackets
You’re looking for a pair of numbers that multiply together to give 10 and add together to give 7.
#15. Fully factorise π₯Β² β 9.
Topic: The Difference of Two Squares
You’re looking for a pair of numbers that multiply together to give -9 and add together to give 0.
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