Question

(A+B+C)^2 is equal to

Answer 1

A2+B2+C2+2AB+2BC+2CA

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Answer 2

Hey there!

That's called a square of a trinomial

 (A+B+C)² = A² + B² + C² + 2AB + 2BC + 2CA 

Derivation: 

In (A+B+C)² , Let B+C= X

So, (A+B+C)²  becomes  (A+ X)²

Here we use the identity (A+B)²= A² + B² + 2AB

Which means, (A+X)²= A² + X² + 2AX

Substituting X with B+C.

(A+B+C)²= A² + (B+C)² + 2A(B+C)
               = A² + B² + C² + 2BC + 2AB + 2AC

And so we get the identity, 

(A+B+C)² = A² + B² + C² + 2AB + 2BC + 2CA