Question -
Answer -
(i)┬а(96)3
We have,
(96)3
Let us express thegiven expression as two different entities and apply the binomial theorem.
(96)3┬а=(100 тАУ 4)3
=┬а3C0┬а(100)3┬а(4)0┬атАУ┬а3C1┬а(100)2┬а(4)1┬а+┬а3C2┬а(100)1┬а(4)2┬атАУ┬а3C3┬а(100)0┬а(4)3
= 1000000 тАУ 120000 +4800 тАУ 64
= 884736
(ii)┬а(102)5
We have,
(102)5
Let us express thegiven expression as two different entities and apply the binomial theorem.
(102)5┬а=(100 + 2)5
=┬а5C0┬а(100)5┬а(2)0┬а+┬а5C1┬а(100)4┬а(2)1┬а+┬а5C2┬а(100)3┬а(2)2┬а+┬а5C3┬а(100)2┬а(2)3┬а+┬а5C4┬а(100)1┬а(2)4┬а+┬а5C5┬а(100)0┬а(2)5
= 10000000000 +1000000000 + 40000000 + 800000 + 8000 + 32
= 11040808032
(iii)┬а(101)4
We have,
(101)4
Let us express thegiven expression as two different entities and apply the binomial theorem.
(101)4┬а=(100 + 1)4
=┬а4C0┬а(100)4┬а+┬а4C1┬а(100)3┬а+┬а4C2┬а(100)2┬а+┬а4C3┬а(100)1┬а+┬а4C4┬а(100)0
= 100000000 + 4000000+ 60000 + 400 + 1
= 104060401
(iv)┬а(98)5
We have,
(98)5
Let us express thegiven expression as two different entities and apply the binomial theorem.
(98)5┬а=(100 тАУ 2)5
=┬а5C0┬а(100)5┬а(2)0┬атАУ┬а5C1┬а(100)4┬а(2)1┬а+┬а5C2┬а(100)3┬а(2)2┬атАУ┬а5C3┬а(100)2┬а(2)3┬а+┬а5C4┬а(100)1┬а(2)4┬атАУ┬а5C5┬а(100)0┬а(2)5
= 10000000000 тАУ1000000000 + 40000000 тАУ 800000 + 8000 тАУ 32
= 9039207968