WAEC - Mathematics (2016 - No. 14)

Factorize; (2x + 3y)2 - (x - 4y)2
(3x - y)(x + 7y)
(3x + y)(2x - 7y)
(3x + y)(x - 7y)
(3x - y)(2x + 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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