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Grade 5 · Foundation and Higher · free GCSE maths worksheet

Expanding double brackets

Expanding (x + a)(x + b).

16 original questions, 48 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Expand and simplify  (x + 4)(x + 6)

2 marks
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x2 + 10x + 24
2

Expand and simplify  (x - 3)(x + 8)

2 marks
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x2 + 5x - 24
3

Expand and simplify (x − 4)(x − 6)

2 marks
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x2 - 10x + 24
4

Expand and simplify (x + 7)2

2 marks
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x2 + 14x + 49
5

Expand and simplify (x − 5)2

2 marks
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x2 - 10x + 25
6

Expand and simplify (2x + 3)(x + 4)

3 marks
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2x2 + 11x + 12
7

A square has sides of length (x + 3) cm.
Show that the area of the square is (x2 + 6x + 9) cm2.

3 marks
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(x + 3)(x + 3) = x2 + 6x + 9
8

Expand and simplify (2x + 3)(3x − 1)

3 marks
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6x2 + 7x - 3
9

Expand and simplify (3x − 2)(2x − 5)

3 marks
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6x2 - 19x + 10
10

Expand and simplify (2x − 1)2

3 marks
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4x2 - 4x + 1
11

Expand and simplify (x + 3)(x + 4) + (x + 1)(x + 2)

4 marks
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2x2 + 10x + 14
12

Expand and simplify (x + 6)(x − 2) − (x + 1)(x − 3)

4 marks
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6x - 9
13

A rectangular card measures (x + 5) cm by (x + 3) cm.

A square of side x cm is cut from the card.

Show that the area of card remaining is (8x + 15) cm2.

(x + 5) cm(x + 3) cmx cmx cmCut outDiagram NOT accurately drawn
3 marks
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(x + 5)(x + 3) - x2 = x2 + 8x + 15 - x2 = 8x + 15
14
  1. Expand and simplify  (x + 9)(x - 2)
  2. Factorise  x2 - 3x - 28
4 marks
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a) x2 + 7x - 18 b) (x - 7)(x + 4)
15
  1. Expand and simplify  (2x + 3)(x - 4)
  2. Factorise fully  6y2 + 9y
4 marks
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a) 2x2 - 5x - 12 b) 3y(2y + 3)
16
  1. Expand and simplify  (y + 7)(y - 7)
  2. Factorise  x2 + x - 30
4 marks
Show answer
a) y2 - 49 b) (x + 6)(x - 5)

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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