8. (101)4
The given expression ( 101 ) 4 .
The formula for binomial expansion is ,
. ( a + b ) n = C n 0 a n + C n 1 a n − 1 b + C n 2 a n − 2 b 2 + .......... + C n n − 1 a . b n − 1 + C n n b n (1)
To apply the binomial theorem, power of expression is easier to calculate so we can write sum or difference of two number which is equal to 101 .
101 = 100 + 1 (2)
On comparing the equations (1) and (2), values of a = 100 , b = 1 and n = 4 .
( 101 ) 4 = ( 100 + 1 ) 4 = C 4 0 ( 100 ) 4 ( 1 ) 1 + C 4 1 ( 100 ) 3 ( 1 ) 2 + C 4 2 ( 100 ) 2 ( 1 ) 3 + C 4 3 ( 100 ) ( 1 ) 4 = ( 100 ) 4 + 4 ( 100 ) 3 + 6 ( 100 ) 2 + 4 ( 100 ) + ( 1 ) 4 = 104060401
Thus ( 101 ) 4 is equal to 104060401.
The given expression
The formula for binomial expansion is ,
.
To apply the binomial theorem, power of expression is easier to calculate so we can write sum or difference of two number which is equal to
On comparing the equations (1) and (2), values of
Thus
