# 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)

(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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