State True or False.
$(2 x - y + z)^{2}$ $= 4 x^{2} + y^{2} + z^{2} - 4 x y - 2 y z + 4 z x$

True

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False

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Solution

The correct option is A True
Simplify given expression,
$∵ (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 a c$
$(2 x - y + z)^{2} = [2 x + (- y) + z]^{2} = (2 x)^{2} + (- y)^{2} + (z)^{2} + 2 (2 x) (- y) + 2 (- y) (z) + 2 (z) (2 x)$
$= 4 x^{2} + y^{2} + z^{2} - 4 x y - 2 y z + 4 z x$
Hence, given statement is true.
Hence the correct answer is A.

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