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Factorise : (a - b)^3 + (b - c)^3 + (c -
Question
Factorise :
(
a
β
b
)
3
+
(
b
β
c
)
3
+
(
c
β
a
)
3
.
A
3
a
2
(
b
β
c
)
+
3
b
2
(
c
β
a
)
+
3
c
2
(
a
β
b
)
B
a
2
(
c
β
b
)
+
b
2
(
a
β
c
)
+
c
2
(
b
β
c
)
C
3
a
2
(
c
β
b
)
+
3
b
2
(
a
β
c
)
+
3
c
2
(
b
β
a
)
D
3
a
(
c
β
b
)
+
3
b
(
a
β
c
)
+
3
c
(
b
β
c
)
Easy
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Updated on : 2022-09-05
Solution
Verified by Toppr
Correct option is C)
We know,Β
(
a
β
b
)
3
=
a
3
β
b
3
β
3
a
2
b
+
3
a
b
2
βΉ
Β Β
(
a
β
b
)
3
=
a
3
β
b
3
β
3
a
b
(
a
β
b
)
.
Then,
(
a
β
b
)
3
+
(
b
β
c
)
3
+
(
c
β
a
)
3
=
(
a
3
β
3
a
2
b
+
3
a
b
2
β
b
3
)
+
(
b
3
β
3
b
2
c
+
3
b
c
2
β
c
3
)
+
(
c
3
β
3
c
2
a
+
3
c
a
2
β
a
3
)
=
β
3
a
2
b
+
3
a
b
2
β
3
b
2
c
+
3
b
c
2
β
3
c
2
a
+
3
c
a
2
=
3
a
2
(
c
β
b
)
+
3
b
2
(
a
β
c
)
+
3
c
2
(
b
β
a
)
.
Therefore, option
C
is correct.
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