State true or false, if the expansion of the following expression is:
$(9 x + 2 y + z)^{2} = 81 x^{2} + 4 y^{2} + z^{2} + 36 x y + 4 y z + 18 z x$

True

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False

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Solution

The correct option is A True
We know that,
$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
So,
$(9 x + 2 y + z)^{2} = (9 x)^{2} + (2 y)^{2} + (z)^{2} + 2 \times (9 x) \times (2 y) + 2 \times (2 y) \times (z) + 2 \times (z) \times (9 x)$
$(9 x + 2 y + z)^{2} = 81 x^{2} + 4 y^{2} + z^{2} + 36 x y + 4 y z + 18 z x$

Hence the answer is true

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