Evaluate :


To find: Value of


Formula used: (i)


(ii) (a+b)n = nC0an + nC1an-1b + nC2an-2b2 + …… +nCn-1abn-1 + nCnbn


(a+b)6 = 6C0a6 + 6C1a6-1b + 6C2a6-2b2 + 6C3a6-3b3 + 6C4a6-4b4 + 6C5a6-5b5 + 6C6b6


6C0a6 + 6C1a5b + 6C2a4b2 + 6C3a3b3 + 6C4a2b4 + 6C5ab5 + 6C6b6 … (i)


(a-b)6


6C0a6 - 6C1a5b + 6C2a4b2 - 6C3a3b3 + 6C4a2b4 - 6C5ab5 + 6C6b6 … (ii)


Substracting (ii) from (i)


(a+b)6 - (a-b)6 = [6C0a6 + 6C1a5b + 6C2a4b2 + 6C3a3b3 + 6C4a2b4 + 6C5ab5 + 6C6b6] – [6C0a6 - 6C1a5b + 6C2a4b2 - 6C3a3b3 + 6C4a2b4 - 6C5ab5 + 6C6b6]


= 2[6C1a5b + 6C3a3b3 + 6C5ab5]


= 2


= 2[(6)a5b + (20)a3b3 + (6)ab5]


(a+b)6 - (a-b)6 = 2[(6)a5b + (20)a3b3 + (6)ab5]


Putting the value of a = and b = in the above equation



2


2



Ans)


2