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4 (a) Factorise - OCR - GCSE Maths - Question 4 - 2017 - Paper 1

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4 (a) Factorise. x^2 - 43^2 (b) Calculate. 57^2 - 43^2

Worked Solution & Example Answer:4 (a) Factorise - OCR - GCSE Maths - Question 4 - 2017 - Paper 1

Step 1

Factorise.

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Answer

To factorise the expression x2−432x^2 - 43^2, we recognize this as a difference of squares, which follows the formula: a2−b2=(a−b)(a+b)a^2 - b^2 = (a - b)(a + b)

In this case, let:

  • a=xa = x
  • b=43b = 43

Thus, we can rewrite the expression as: x2−432=(x−43)(x+43)x^2 - 43^2 = (x - 43)(x + 43)

Step 2

Calculate.

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Answer

To evaluate 572−43257^2 - 43^2, we again use the difference of squares formula: 572−432=(57−43)(57+43)57^2 - 43^2 = (57 - 43)(57 + 43)

Calculating the components:

  • 57−43=1457 - 43 = 14
  • 57+43=10057 + 43 = 100

Therefore: 572−432=14imes100=140057^2 - 43^2 = 14 imes 100 = 1400

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