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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. $x^2 - 43^2$

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Answer

The given expression is a difference of squares, which can be factored using the identity:

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, the factorization is:

(x−43)(x+43)(x - 43)(x + 43)

Step 2

Calculate. $57^2 - 43^2$

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Answer

This is also a difference of squares:

Using the identity again, we have:

572−432=(57−43)(57+43)57^2 - 43^2 = (57 - 43)(57 + 43)

Calculating the factors:

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

Thus, we calculate:

14imes100=140014 imes 100 = 1400

Therefore, the result is 14001400.

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