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JAMB Mathematics 1993 Question 13

Question 13

Algebraic Expressions

Evaluate (x + 1/x + 1)2 − (x − 1/x − 1)2

  1. A.4x2
  2. B.(2/x + 2)2
  3. C.4
  4. D.4(1 + x)
Show the answer and explanation

Answer: D (4(1 + x))

Explanation

Use a² − b² = (a + b)(a − b). Here a + b = 2x and a − b = 2/x + 2, so the product is 2x(2/x + 2) = 4 + 4x = 4(1 + x).