Evaluate :


To find: Value of


Formula used: (i)


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


(a+b)7 =


7C0a7 + 7C1a6b + 7C2a5b2 + 7C3a4b3 + 7C4a3b4 + 7C5a2b5 + 7C6a1b6 + 7C7b7 … (i)


(a-b)7 =


7C0a7 - 7C1a6b + 7C2a5b2 - 7C3a4b3 + 7C4a3b4 - 7C5a2b5 + 7C6a1b6 - 7C7b7 … (ii)


Adding eqn. (i) and (ii)


(a+b)7 + (a-b)7 = [7C0a7 + 7C1a6b + 7C2a5b2 + 7C3a4b3 + 7C4a3b4 + 7C5a2b5 + 7C6a1b6 + 7C7b7] + [7C0a7 - 7C1a6b + 7C2a5b2 - 7C3a4b3 + 7C4a3b4 - 7C5a2b5 + 7C6a1b6 - 7C7b7]


2[7C0a7 + 7C2a5b2 + 7C4a3b4 + 7C6a1b6]


2


2[(1)a7 + (21)a5b2 + (35)a3b4 + (7)ab6]


2[a7 + 21a5b2 + 35a3b4 + 7ab6] = (a+b)7 + (a-b)7


Putting the value of a = 2 and b = in the above equation



= 2


= 2[128 + 21(32)(3)+ 35(8)(9) + 7(2)(27)]


= 2[128 + 2016 + 2520 + 378]


= 10084


Ans) 10084


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