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: Option A
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)