Ex 8.2, 4 - Write general term of (x2 - yx)12 - Binomial - Ex 8.2

  1. Chapter 8 Class 11 Binomial Theorem
  2. Serial order wise
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Ex 8.2, 4 Write the general term in the expansion of (x2 – yx)12, x ≠ 0 We know that General term of expansion (a + b)n is Tr+1 = nCr an–r br For (x2 – yx), Putting n = 12, a = x2 , b = – yx Tr+1 = 12Cr (x2)12–r . (– yx)r = ﷐12!﷮𝑟!﷐12 − 𝑟 ﷯!﷯ . (x)2(12–r) . (–1)r . yr . xr = ﷐12!﷮𝑟!﷐12 − 𝑟 ﷯!﷯ . x24 – 2r . (–1)r . yr . xr = ﷐12!﷮𝑟!﷐12 − 𝑟 ﷯!﷯. x24 – 2r .xr . yr . (–1)r = (-1)r . ﷐12!﷮𝑟!﷐12 − 𝑟 ﷯!﷯ . (x)24 – 2r + r . yr = (-1)r . ﷐12!﷮𝑟!﷐12 − 𝑟 ﷯!﷯ . x24 – r . yr = (-1)r . 12Cr x24 – r . yr Hence, General term = (-1)r . 12Cr x24 – r . yr

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