Factorize; (2x + 3y)2 - (x - 4y)2

  • A (3x - y)(x + 7y)
  • B (3x + y)(2x - 7y)
  • C (3x + y)(x - 7y)
  • D (3x - y)(2x + 7y)
waec 2016mathematics

The correct answer is A. (3x - y)(x + 7y)

(2x + 3y)2 - (x - 4y)2

= (2x + 3y)(2x + 3y) - (x - 4y)(x - 4y)

= 4x2 + 12xy + 9y2 - (x2 - 8xy+ 16y2)

= 4x2 + 12xy + 19y2 - x2 + 8xy - 16y2

= 3x2 + 20xy - 7y2

= 3x2 + 21xy - xy - 7y2

= 3x(x + 7y) - y(x + 7y)

= (3x - y)(x + 7y)

Previous question Next question