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What is the value of the given expression (a + b + c)2 - a2-b2-c2?
Question

What is the value of the given expression (a + b + c)2 - a2-b2-c2?

A.

2abc

B.

2(ab + bc + ca)

C.

2(a + b + c)

D.

2ab + bc - 2ca

Correct option is B

Given:
(a + b + c)2 - a2-b2-c2
Formula Used:
(a + b + c)2= a2 + b2 + c2 + 2(ab + bc + ca)
Solution:
(a + b + c)2 - a2 - b2 - c2
=a2 + b2 + c2 + 2(ab + bc + ca) - a2 - b2 - c2
=2(ab + bc + ca)
Alternate Method:
Concept: Value putting method
Let a=2 , b=1, c=1
(a + b + c)2 - a2-b2-c2=(2+1+1)2-22-12-12 =16-6=10
Now by checking option (b)
2(ab + bc + ca) = 2 (2×1+1×1+2×1) = 2 (2+1+2) = 2×5 = 10
L.H.S = R.H.S

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