The expansion of $(a − 2 b − 3 c) 2$ is ____

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Detailed Solution

The expansion of

(a − 2 b − 3 c) 2

a 2 + 4 b 2 + 9 c 2 − 4 a b + 12 b c − 6 c a

.
According to the given information, a polynomial is given as

a − 2 b − 3 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,

⇒ a − 2 b − 3 c 2 = a 2 + − 2 b 2 + − 3 c 2 + 2 × a × − 2 b + 2 × − 2 b × − 3 c + 2 × − 3 c × a ⇒ a + 2 b + 5 c 2 = a 2 + 4 b 2 + 9 c 2 − 4 a b + 12 b c − 6 c a

Therefore, the expansion of

a − 2 b − 3 c 2

a 2 + 4 b 2 + 9 c 2 − 4 a b + 12 b c − 6 c a

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