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Question

Evaluate (a+2b+3c)2


A

a2+4b2+9c2+4ab+12bc+6ac

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B

a2+4b2+9c2+4ab+12bc+12ac

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C

a2+4b2+9c2+8ab+12bc+6ac

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D

a2+4b2+9c3+4ab+12bc+6ac

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Solution

The correct option is A

a2+4b2+9c2+4ab+12bc+6ac


We use the identity (a+b+c)2 = a2+b2+c2+2ab+2bc+2ca

Replacing the value of a,b,and c with a,2b, and 3c respectively.

We get (a+2b+3c)2 = a2+(2b)2+(3c)2+4ab+12bc+6ac

= a2+4b2+9c2+4ab+12bc+6ac


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Algebraic Identity: (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ac
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