Question : The algebraic expression $4x^2-y^2+6y-9$ is equal to______.
Option 1: $(2x + y - 3)(2x - y + 3)$
Option 2: $(2x - y - 3)(2x - y + 3)$
Option 3: $(2x + y - 3)^2$
Option 4: $(2x + y + 3)^2$
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Correct Answer: $(2x + y - 3)(2x - y + 3)$
Solution :
$4x^2-y^2+6y-9$
$= 4x^2-(y^2-6y+9)$
$= (2x)^2-(y-3)^2$
$= (2x+y-3)(2x-y+3)$
Hence, the correct answer is $(2x+y-3)(2x-y+3)$.
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