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Ex 8.1, 8 - Using Binomial Theorem, evaluate (101)4 - Chapter 8 - Ex 8.1

  1. Chapter 8 Class 11 Binomial Theorem
  2. Serial order wise
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Ex 8.1,8 Using Binomial Theorem, evaluate (101)4 (101)4 = (100 + 1)4 We know that (a + b)n = nC0 an b0 + nC1 an – 1 b1 + nC2 an – 2 b2 + …. …. + nCn – 1 a1 bn – 1 + nCn a0 bn Hence, (a + b)4 = 4C0 a4 (b)0 + 4C1 a3 b1 + 4C2 a2 b2 + 4C3 a1b3 + 4C4 a0 b4 = ﷐4!﷮0!﷐ 4 − 0﷯!﷯ a4 × 1 + ﷐4!﷮1×(4−1)!﷯ a2 b2 + ﷐4!﷮2!﷐4 −2﷯!﷯ ab3 + ﷐4!﷮4!(4 − 4)!﷯ 1 × b4 = ﷐4!﷮1 ×4!﷯ a4 + ﷐4!﷮1 ×3!﷯ a3 b + ﷐4!﷮2!(4 − 2)!﷯ a2 b2 + ﷐4!﷮3!﷐4 −3﷯! ﷯ ab3 + ﷐4!﷮4! 0!﷯ b4 = a4 + 4a3 b + 6a2 b2 + 4 ab3 + b4 Hence, (a + b)4 = a4 + 4a3 b + 6a2 b2 + 4 ab3 + b4 We need to find (100 + 1)4, Putting a = 100 & b = 1 (100 + 1)4 = (100)4 + 4 (100)3 (1) + 6 (100)2 (1)2 + 4 (100) (1)3+ (1)4 (101)4 = (100000000) + 4(1000000) + 6(10000) + 4(100) + 1 = 100000000 + 4000000 + 60000 + 400 = 104060401 So, (101)4 = 104060401

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