1.

Using binomial theorem evaluate each of the following:(i) (96)3(ii) (102)5(iii) (101)4(iv) (98)5

Answer»

(i) We have,

(96)3

Lets express the given expression as two different entities and apply the binomial theorem.

(96)3 = (100 – 4)3

= 3C0 (100)3 (4)0 – 3C1 (100)2 (4)1 + 3C2 (100)1 (4)2 – 3C3 (100)0 (4)3

= 1000000 – 120000 + 4800 – 64

= 884736

(ii) We have,

(102)5

Lets express the given expression as two different entities and apply the binomial theorem.

(102)5 = (100 + 2)5

= 5C0 (100)5 (2)0 + 5C1 (100)4 (2)1 + 5C2 (100)3 (2)2 + 5C3 (100)2 (2)3 + 5C4 (100)1 (2)4 + 5C5 (100)0 (2)5

= 10000000000 + 1000000000 + 40000000 + 800000 + 8000 + 32

= 11040808032

(iii) We have,

(101)4

Lets express the given expression as two different entities and apply the binomial theorem.

(101)4 = (100 + 1)4

= 4C0 (100)4 + 4C1 (100)3 + 4C2 (100)2 + 4C3 (100)1 + 4C4 (100)0

= 100000000 + 4000000 + 60000 + 400 + 1

= 104060401

(iv) We have,

(98)5

Lets express the given expression as two different entities and apply the binomial theorem.

(98)5 = (100 – 2)5

= 5C0 (100)5 (2)0 – 5C1 (100)4 (2)1 + 5C2 (100)3 (2)2 – 5C3 (100)2 (2)3 + 5C4 (100)1 (2)4 – 5C5 (100)0 (2)5

= 10000000000 – 1000000000 + 40000000 – 800000 + 8000 – 32

= 9039207968


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