Which of the following is an identity?

(c + 2) (c + 2) = c^{2} + 4 + 4 c

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(c + 2) (c + 2) = c^{2} + 4 + 2 c

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(c - 2) (c + 2) = c^{2} + 4 + 4 c

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None of these

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Solution

The correct option is A $(c + 2) (c + 2) = c^{2} + 4 + 4 c$
Identity Equation: An equation which is true for every value of the variable is called an identity equation.
Example of Identity Equation : $5 (a - 3) = 5 a - 15$
In option A, $(c + 2) (c + 2) = c^{2} + 4 + 4 c$ [since, $(x + y) (a + b) = (x a + x b + y a + y b)$ ]
$L H S = c . c + 2. c + 2. c + 2.2$
$= c^{2} + 4 c + 4$
$= R H S$
In option B, $(c + 2) (c + 2) = c^{2} + 4 + 2 c$
$L H S = c . c + 2. c + 2. c + 2.2$
$= c^{2} + 4 c + 4$
$\neq R H S$
In option C, $(c - 2) (c + 2) = c^{2} + 4 + 4 c$
$L H S = c . c + 2. c - 2. c - 2.2$
$= c^{2} + 0 - 4$
$= c^{2} - 4$
$\neq R H S$
Only option A satisfies the law of Identity.

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