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Grade 6 · Higher · free GCSE maths worksheet

Difference of two squares

Factorising x^2 - a^2.

12 original questions, 36 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

Factorise  x2 - 49

1 mark
Show answer
(x + 7)(x - 7)
2
  1. Factorise m2 − 64
  2. Factorise k2 − 100
2 marks
Show answer
a) (m - 8)(m + 8) b) (k - 10)(k + 10)
3

Factorise 4x2 − 25

2 marks
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(2x - 5)(2x + 5)
4

Use the difference of two squares to work out these without a calculator.

  1. 992 − 12
  2. 732 − 272
3 marks
Show answer
a) 9800 b) 4600
5

Factorise fully 2x2 − 50

3 marks
Show answer
2(x - 5)(x + 5)
6

Simplify fully x2 − 92x + 6

3 marks
Show answer
(x - 3)/2
7

Solve 4x2 − 49 = 0

3 marks
Show answer
x = 7/2 or x = -7/2
8

Without working out the squares, show that

532 - 472 = 600

3 marks
Show answer
532 - 472 = (53 + 47)(53 - 47) = 100 x 6 = 600
9

Simplify fully x2 − 16x2 + x − 12

4 marks
Show answer
(x - 4)/(x - 3)
10

Show that (2n + 1)2 − (2n − 1)2 is a multiple of 8 for every integer n.

3 marks
Show answer
8n
11
  1. Factorise y2 - 25
  2. Hence, or otherwise, expand and simplify (y + 5)(y - 5)(2y + 3)
5 marks
Show answer
a) (y + 5)(y - 5) b) 2y3 + 3y2 - 50y - 75
12
  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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