Find the missing value to proof the identity: $(2 x + y) (2 x - y) = (2 x)^{2} - y^{2}$ .

y^{2}

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y (2 x - y)

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2 x (2 x - y)

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(2 x)^{2}

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Solution

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

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