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JAMB Mathematics 1988 Question 17

Question 17

Algebraic Expressions

Factorize completely (x2 + x)2 − (2x + 2)2

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

Answer: D ((x + 1)2(x + 2)(x − 2))

Explanation

Use difference of two squares: (x² + 3x + 2)(x² − x − 2) = (x + 1)(x + 2)(x − 2)(x + 1) = (x + 1)²(x + 2)(x − 2).