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Is it true that $4 a 2 + b 2 + c 2 − 4 a b − 2 b c + 4 a c$ is the expansion of $(2 a − b + c) 2$ ?

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True

False

answer is A.

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Detailed Solution

According to the given information, a polynomial is given as

2 a − b + c 2

.
Using the equation

a + b + c 2 = a 2 + b 2 + c 2 + 2 a b + 2 b c + 2 c a

to expand the given polynomial, we get,

⇒ 2 a − b + c 2 = 2 a 2 + − b 2 + c 2 + 2 × 2 a × − b + 2 × − b × c + 2 × c × 2 a ⇒ 2 a − b + c 2 = 4 a 2 + b 2 + c 2 − 4 a b − 2 b c + 4 a c

Therefore, the expansion of

2 a − b + c 2

4 a 2 + b 2 + c 2 − 4 a b − 2 b c + 4 a c

.
The given statement is true.
Hence, option 1 is correct.

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