Expand using identities: $(x y + 3 z)^{2}$

x^{2} y^{2} + 6 x y z - z^{2}

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x^{2} y + 6 x z + 9 z^{2}

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x y^{2} - 6 x y z + 9 z^{2}

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x^{2} y^{2} + 6 x y z + 9 z^{2}

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Solution

The correct option is D $x^{2} y^{2} + 6 x y z + 9 z^{2}$
$(x y + 3 z)^{2}$
Using, $(a + b)^{2} = a^{2} + b^{2} + 2 a b$
$= (x y)^{2} + (3 z)^{2} + 2 (x y) (3 z)$
$= x^{2} y^{2} + 9 z^{2} + 6 x y z$

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