State true or false:
$(2 a + b)^{2} - (2 b + a)^{2} = 3 (a^{2} - b^{2})$ is an identity.

True

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False

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Solution

The correct option is A True
$L . H . S = (2 a + b)^{2} - (2 b + a)^{2} = (4 a^{2} + b^{2} + 4 a b) - (4 b^{2} + a^{2} + 4 a b)$
$= 3 a^{2} - 3 b^{2}$
$= 3 (a^{2} - b^{2})$ $= R . H . S$ .
Since, $L . H . S = R . H . S$ .
Then, clearly, $(2 a + b)^{2} - (2 b + a)^{2} = 3 (a^{2} - b^{2})$ is an identity.
Therefore, option $A$ is true.

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