Question : Simplify:
$(2 a-3 b-c)^2-(a+2 b+c)^2$
Option 1: $3 a^2+5 b^2-16 a b+2 b c-8 a c$
Option 2: $3 a^2+5 b^2-8 a b+2 b c-6 a c$
Option 3: $3 a^2+5 b^2-16 a b-6 a c$
Option 4: $3 a^2+5 b^2-16 a b+2 b c-6 a c$
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Correct Answer: $3 a^2+5 b^2-16 a b+2 b c-6 a c$
Solution :
$(2 a-3 b-c)^2-(a+2 b+c)^2$
= $(4a^2+9b^2+c^2-12ab-4ac+6bc)-(a^2+4b^2+c^2+4ab+2ac+4bc)$
= $3a^2+5b^2-16ab-6ac+2bc$
Hence, the correct answer is $3a^2+5b^2-16ab+2bc-6ac$.
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