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)

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