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Byju's Answer
Standard VIII
Mathematics
Multiplication of Binomial by a Binomial
Simplify: (x3...
Question
Simplify: (x3-y3)3+(y3-z3)3+(z3-x3) 3 divided by (x-y)3+(y-z)3+(z-x)3
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Solution
We
know
that
,
if
a
+
b
+
c
=
0
,
then
a
3
+
b
3
+
c
3
-
3
abc
=
0
or
a
3
+
b
3
+
c
3
=
3
abc
For
the
numerator
:
(
x
3
-
y
3
)
+
(
y
3
-
z
3
)
+
(
z
3
-
x
3
)
=
0
so
,
(
x
3
-
y
3
)
3
+
(
y
3
-
z
3
)
3
+
(
z
3
-
x
3
)
3
=
3
(
x
3
-
y
3
)
(
y
3
-
z
3
)
(
z
3
-
x
3
)
Again
,
x
3
-
y
3
=
(
x
-
y
)
(
x
2
+
xy
+
y
2
)
so
,
(
x
3
-
y
3
)
3
+
(
y
3
-
z
3
)
3
+
(
z
3
-
x
3
)
3
=
3
(
x
-
y
)
(
x
2
+
xy
+
y
2
)
(
y
-
z
)
(
y
2
+
yz
+
z
2
)
(
z
-
x
)
(
z
2
+
zx
+
x
2
)
For
the
denominator
:
(
x
-
y
)
+
(
y
-
z
)
+
(
z
-
x
)
=
0
so
,
(
x
-
y
)
3
+
(
y
-
z
)
3
+
(
z
-
x
)
3
=
3
(
x
-
y
)
(
y
-
z
)
(
z
-
x
)
Now
,
(
x
3
-
y
3
)
3
+
(
y
3
-
z
3
)
3
+
(
z
3
-
x
3
)
3
(
x
-
y
)
3
+
(
y
-
z
)
3
+
(
z
-
x
)
3
=
3
(
x
-
y
)
(
x
2
+
xy
+
y
2
)
(
y
-
z
)
(
y
2
+
yz
+
z
2
)
(
z
-
x
)
(
z
2
+
zx
+
x
2
)
3
(
x
-
y
)
(
y
-
z
)
(
z
-
x
)
=
(
x
2
+
xy
+
y
2
)
(
y
2
+
yz
+
z
2
)
(
z
2
+
zx
+
x
2
)
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1
Similar questions
Q.
If
x
+
y
+
z
=
0
, what can be said about
x
3
+
y
3
+
z
3
?
Q.
Simplify :
(x-y)
3
+ (y-z)
3
+ (z-x)
3
Q.
Prove that:
(x + y)
3
+ (y + z)
3
+ (z + x)
3
− 3(x + y) (y + z) (z + x) = (x
3
+ y
3
+ z
3
− 3xyz).
Q.
Factorize:
(
x
−
y
)
3
+
(
y
−
z
)
3
+
(
z
−
x
)
3
Q.
Factorise:
(
x
−
y
)
3
+
(
y
−
z
)
3
+
(
z
−
x
)
3
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