Factorize; (2x + 3y) 2 - (x - 4y) 2
MATHEMATICS
WAEC 2016
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)
Correct Answer: A. (3x - y)(x + 7y)
Explanation
(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)
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