Expand using identity : $(x - 2 y + 6) (x - 2 y - 6)$

x^{3} - 4 x y + 4 y^{2} - 16

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x^{2} + 4 x y + y^{2} - 12

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x^{2} - 4 x y + 4 y^{2} - 36

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x^{3} - 4 x y + y^{2} - 6

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Solution

The correct option is D $x^{2} - 4 x y + 4 y^{2} - 36$
$(x - 2 y + 6) (x - 2 y - 6)$
$= (x - 2 y)^{2} - (6)^{2}$
Using,
$(a - b)^{2} = a^{2} - 2 a b + b^{2})$
$= [(x)^{2} - 2 (x) (2 y) + (2 y)^{2}] - (6)^{2}$
$= x^{2} - 4 x y + 4 y^{2} - 36$

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