Question

6. (96)*

Answer 1

The given expression ( 96 ) 3 .

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 96 .

96=100−4 (2)

On comparing the equations (1) and (2), values of a=100, b=−4 and n=3 .

( 96 ) 3 = ( 100−4 ) 3 = C 3 0 ( 100 ) 3 − C 3 1 ( 100 ) 2 ( 4 )+ C 3 2 ( 100 ) ( 4 ) 2 − C 3 3 ( 4 ) 3 = ( 100 ) 3 −3 ( 100 ) 2 ( 4 )+3( 100 ) ( 4 ) 2 − ( 4 ) 3 =1000000−120000+4800−64 =884736

Thus , ( 96 ) 3 is equal to 884736.