Expanding double brackets: GCSE and IGCSE Maths Practice
Expanding and factorising
Expanding double brackets
43 self-marking GCSE and IGCSE practice questions on Expanding double brackets, written specifically for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Foundation and Higher and Core and Extended tier. Instant marking with full worked solutions on every question.
A few of the 43 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 13 marksGrade 4-5
A rectangular lawn has a width of (x+2) m and a length of (x+6) m.
Find an expression for its area, in the form ax2+bx+c
What are the common mistakes in Expanding double brackets?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Omits the cross terms when expanding brackets (e.g. missing terms in (a+b)^2)
Only multiplied the first term by the first term and the last term by the last term, missing the two cross-product x terms that must be added to give the middle term
Mishandles a sign when multiplying out brackets
Made a sign error on one of the two cross-product terms when combining them into the middle term
Multiplies only the first and last terms when expanding two brackets, missing the two cross terms
Multiplies only the first terms (x×x) and last terms (1×9
Quick answers about Expanding double brackets
How many Expanding double brackets practice questions are there?
There are 43 self-marking GCSE and IGCSE Maths questions on Expanding double brackets, written for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Foundation and Higher and Core and Extended tier. Each one is marked instantly and has a full worked solution.
Do I need an account to practise Expanding double brackets?
No. You can start practising Expanding double brackets straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.
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Show the worked solution
Area = length × width: (x+6)(x+2)
Multiply every term in the first bracket by every term in the second bracket (FOIL): x×x=x2, x×2=2x, 6×x=6x, 6×2=12M1
x2+2x+6x+12M2
Collect like terms: x2+8x+12A1
Question 23 marksGrade 4-5
A vegetable plot has a width of (x+1) m and a length of (x+9) m.
Find an expression for its area, in the form ax2+bx+c.
Show the worked solution
Area = length × width: (x+9)(x+1)
Multiply every term in the first bracket by every term in the second bracket (FOIL): x×x=x2
Question 34 marksGrade 4-5
(a) Expand and simplify (x+4)(x+8).
(b) Hence write down the two solutions of (x+4)(x+8)=0.
(b)(i) The smaller solution.
(b)(ii) The larger solution.
Question 43 marksGrade 6-7
An L-shaped patio is made from a large rectangle with a width of x+8 m and a length of x+5 m, with a smaller rectangular section with a width of 3 m and a length of x m cut from one corner.
Find an expression for the area of the shape, in the form ax2+bx+c.
Question 53 marksGrade 6-7
An L-shaped garden is made from two adjoining rectangles. The first has a width of x+3 m and a length of x+7 m. The second has a width of 5 m and a length of x m.
Find an expression for the total area of the shape, in the form ax2+bx+c.
Question 64 marksGrade 8
The area of a rectangle with sides (3x+2) and (x+c) can be written as ax2+bx−10.
Find the values of a, b and c.