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Byju's Answer
Standard XII
Mathematics
Algebra of Complex Numbers
Prove that a+...
Question
Prove that
a
+
b
+
c
3
-
a
3
-
b
3
-
c
3
=
3
a
+
b
b
+
c
c
+
a
Open in App
Solution
a
+
b
+
c
3
=
a
+
b
+
c
3
=
a
+
b
3
+
c
3
+
3
a
+
b
c
a
+
b
+
c
⇒
a
+
b
+
c
3
=
a
3
+
b
3
+
3
a
b
a
+
b
+
c
3
+
3
a
+
b
c
a
+
b
+
c
⇒
a
+
b
+
c
3
-
a
3
+
b
3
-
c
3
=
3
a
b
a
+
b
+
3
a
+
b
c
a
+
b
+
c
⇒
a
+
b
+
c
3
-
a
3
+
b
3
-
c
3
=
3
a
+
b
a
b
+
c
a
+
c
b
+
c
2
⇒
a
+
b
+
c
3
-
a
3
+
b
3
-
c
3
=
3
a
+
b
a
b
+
c
+
c
b
+
c
⇒
a
+
b
+
c
3
-
a
3
+
b
3
-
c
3
=
3
a
+
b
b
+
c
a
+
c
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Similar questions
Q.
Question 9
Prove that
(
a
+
b
+
c
)
3
–
a
3
–
b
3
–
c
3
=
3
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
.
Q.
Question 9
Prove that
(
a
+
b
+
c
)
3
–
a
3
–
b
3
–
c
3
=
3
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
.
Q.
Get the factorisation
(
a
+
b
+
c
)
3
−
a
3
−
b
3
−
c
3
=
3
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
writing the expression
(
a
+
b
+
c
)
3
−
a
3
−
b
3
−
c
3
=
[
(
a
+
b
+
c
)
3
−
a
3
]
−
[
b
3
+
c
3
]
Q.
Prove that:
(
a
+
b
)
3
(
b
+
c
)
3
+
(
c
+
a
)
3
-
3
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
=
2
(
a
3
+
b
3
+
c
3
-
3
a
b
c
)
.
Q.
(
a
+
b
)
3
+
(
b
+
c
)
3
+
(
c
+
a
)
3
−
3
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
3
(
a
3
+
b
3
+
c
3
−
3
a
b
c
)
= ____________
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