What is the missing value to proof the identity: $4 x^{2} - 16 y^{2} = (2 x - 4 y) (2 x + 4 y)$ ?

4 x^{2}

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4 y (2 x - 4 y)

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2 x (2 x - 4 y)

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16 y^{2}

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Solution

The correct option is C $2 x (2 x - 4 y)$
To proof the identity: $4 x^{2} - 16 y^{2} = (2 x - 4 y) (2 x + 4 y)$
Area of full square $=$ area of pink rectangle $+$ area of blue rectangle.
i.e., $4 x^{2} - 16 y^{2} = 2 x (2 x - 4 y) + 4 y (2 x - 4 y)$
$4 x^{2} - 16 y^{2} = (2 x + 4 y) (2 x - 4 y)$
So, the missing value is $4 y (2 x - 4 y)$ .

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