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JAMB Mathematics 2022 Question 17

Question 17

Algebraic Expressions

Factorize completely 4a2 − 12ab − c2 + 9b2?

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

Answer: D ((2a − 3b − c)(2a − 3b + c))

Explanation

Group 4a² − 12ab + 9b² = (2a − 3b)². Then (2a − 3b)² − c² is a difference of two squares: (2a − 3b − c)(2a − 3b + c).