-2a³-[a-b-{a+b+c-(-2a³-2b-3c)}]
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Answer:
We know, (a−b)
3
=a
3
−b
3
−3a
2
b+3ab
2
⟹ (a−b)
3
=a
3
−b
3
−3ab(a−b).
Then,
(a−b)
3
+(b−c)
3
+(c−a)
3
=(a
3
−3a
2
b+3ab
2
−b
3
)+(b
3
−3b
2
c+3bc
2
−c
3
)+(c
3
−3c
2
a+3ca
2
−a
3
)
=−3a
2
b+3ab
2
−3b
2
c+3bc
2
−3c
2
a+3ca
2
=3a
2
(c−b)+3b
2
(a−c)+3c
2
(b−a).
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