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Byju's Answer
Standard VIII
Mathematics
Multiplication of Any Polynomial
Expand: n - ...
Question
Expand:
(
n
−
1
n
)
(
n
+
1
n
)
(
n
2
+
1
n
2
)
Open in App
Solution
As we know the formula
(
a
+
b
)
(
a
−
b
)
=
a
2
−
b
2
So
(
n
−
1
n
)
(
n
+
1
n
)
=
(
n
)
2
−
(
1
n
)
2
=
(
n
)
2
−
(
1
n
2
)
=
(
n
2
−
1
n
2
)
(
n
2
−
1
n
2
)
=
(
n
2
−
1
n
2
)
(
n
2
−
1
n
2
)
=
(
n
2
)
2
−
(
1
n
2
)
2
=
n
4
−
1
n
4
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0
Similar questions
Q.
Simplify:
(
n
−
1
n
)
(
n
+
1
n
)
(
n
2
+
1
n
2
)
Q.
If
n
is odd show that
n
(
n
2
−
1
)
is divisible by
24
.
We have
n
(
n
2
−
1
)
=
n
(
n
−
1
)
(
n
+
1
)
.
Q.
The numbers 1, 2, ... ,
n
2
are arranged in an
n
×
n
array in the following way: Pick n numbers from the array such that any two numbers are in different rows and different columns. then the sum of these numbers are
n
∑
k
=
1
a
k
j
k
=
n
(
n
2
+
1
)
2
.
If true then enter
1
and if false then enter
0
1
2
3
...
n
n+1
n+2
n+3
...
2n
⋮
⋮
n
2
−
n
+
1
n
2
−
n
+
2
n
2
−
n
+
3
...
n
2
Q.
If a variable takes the values
0
,
1
,
2
,
.
.
.
,
n
with corresponding frequencies as binomial coefficients
n
C
0
,
n
C
1
,
.
.
.
,
n
C
n
, then the mean of distribution is
Q.
The value of
n
∑
r
=
1
r
n
C
r
n
C
r
−
1
is
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