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JAMB Mathematics 2001 Question 8

Question 8

Algebraic Expressions

Factorize 4x2 − 9y2 + 20x + 25

  1. A.(2x − 3y)(2x + 3y)
  2. B.(2x + 5)(2x − 9y + 5)
  3. C.(2x − 3y + 5)(2x − 3y − 5)
  4. D.(2x − 3y + 5)(2x + 3y + 5)
Show the answer and explanation

Answer: D ((2x − 3y + 5)(2x + 3y + 5))

Explanation

Group as (4x2 + 20x + 25) − 9y2 = (2x + 5)2 − (3y)2. As a difference of two squares this is (2x + 5 − 3y)(2x + 5 + 3y).