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JAMB Mathematics 1988 Question 18

Question 18

Algebraic Expressions

Simplify (x − y)/(x1/3 − y1/3)

  1. A.x2 + xy + y2
  2. B.x2/3 + x1/3y1/3 + y2/3
  3. C.x2/3 − x1/3y1/3 − y2/3
  4. D.x2 − xy + y2
Show the answer and explanation

Answer: B (x2/3 + x1/3y1/3 + y2/3)

Explanation

Let a = x1/3, b = y1/3. Then x − y = a³ − b³ = (a − b)(a² + ab + b²), so the fraction is a² + ab + b² = x2/3 + x1/3y1/3 + y2/3.