Question : What is the value of $a^2+4 b^2+9 c^2-4 a b+12 b c-6 c a$?
Option 1: $(a+2 b-3 c)^2$
Option 2: $(2a- b-3 c)^2$
Option 3: $(2b-a-3 c)^2$
Option 4: $(a-2 b-3 c)^2$
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Correct Answer: $(a-2 b-3 c)^2$
Solution :
$a^2+4 b^2+9 c^2-4 a b+12 b c-6 c a$
= $a^2+(-2 b)^2+(-3 c)^2+2(-2 a b+6 b c-3 c a)$
= $(a-2b-3c)^2$
Hence, the correct answer is $(a-2b-3c)^2$.
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