(a+b+c)^2-(a-b+c)^2+(a+b-c)^2
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2
Answer:
Correct option is
D
3(a
2
+b
2
+c
2
)−2(bc−ab−ac)
The given expression (a+b+c)
2
+(a−b+c)
2
+(a+b−c)
2
can be simplified as follows:
(a+b+c)
2
+(a−b+c)
2
+(a+b−c)
2
=(a
2
+b
2
+c
2
+2ab+2bc+2ca)+[a
2
+(−b)
2
+c
2
+2a(−b)+2(−b)c+2ca]
+[a
2
+b
2
+(−c)
2
+2ab+2b(−c)+2(−c)a]
(∵(a+b+c)
2
=a
2
+b
2
+c
2
+2ab+2bc+2ca)
=(a
2
+b
2
+c
2
+2ab+2bc+2ca)+(a
2
+b
2
+c
2
−2ab−2bc+2ca)
+(a
2
+b
2
+c
2
+2ab−2bc−2ca)
=3a
2
+3b
2
+3c
2
+2ab−2bc+2ca
=3(a
2
+b
2
+c
2
)−2(bc−ab−ac)
Hence, (a+b+c)
2
+(a−b+c)
2
+(a+b−c)
2
=3(a
2
+b
2
+c
2
)−2(bc−ab−ac)
Answered by
1
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