What is to be added to make $4 x^{2} + 12 x y + 8 y^{2}$ a perfect square?

8 y^{2}

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y^{2}

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- 7 y^{2}

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- 4 y^{2}

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Solution

The correct option is B $y^{2}$
$4 x^{2} + 12 x y + 8 y^{2} = (2 x)^{2} + 2 (2 x) (3 y) + (3 y)^{2} - y^{2} = (2 x + 3 y)^{2} - y^{2}$
Therefore, $y^{2}$ should be added.

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