Expanding and Factorising Quiz – Foundation

Expanding and Factorising Diagnostic Test

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

Well done!! You seem ready to go on this topic. Check out some of our other revision quizzes or have a look at the Expanding and Factorising micro mock.

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 2𝑝(7𝑝 – 5).

Topic: Expanding Single Brackets

Remember, 𝑝 Γ— 𝑝 = 𝑝².

#3. Fully factorise 12𝑦 – 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 – 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‘₯ – 5).

Topic: Expanding and Simplifying Single Brackets

After expanding both brackets, you should get 15π‘₯ οΌ‹Β 21 οΌ‹Β 8π‘₯ – 20. Then, you just collect the like terms.

#6. Simplify
7(2π‘₯ – 3) – 2(3π‘₯ – 1).

Topic: Expanding and Simplifying Single Brackets

Be careful with negatives!Β After expanding both brackets, you should get 14π‘₯ – 21 – 6π‘₯ οΌ‹ 2.

#7. Which one of the following expressions is equivalent to
3(2π‘₯ + 5) – 6(3π‘₯ – 1)?

Topic: Expanding and Simplifying Single Brackets

Expanding the brackets gives 6π‘₯ οΌ‹ 15 – 18π‘₯ οΌ‹ 6. Next, you need to simplify and factorise.Β 

#8. Expand (π‘₯ + 5)(π‘₯ – 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‘₯ – 3π‘₯ – 15.

#9. Expand and simplify
(3π‘₯ – 5)Β².

Topic: Expanding Double Brackets

Remember, a bracket squared means multiplied by itself;
(3π‘₯ – 5)2 = (3π‘₯ – 5)(3π‘₯ – 5)

#10. Fully factorise π‘₯Β² – 5π‘₯ – 14.

Topic: Factorising Quadratics (π‘Ž = 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‘₯ – 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‘₯ – 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 – 11π‘₯ + 18.

Topic: Factorising Quadratics (π‘Ž = 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 – 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.

Check Score

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