The fourth term in the expansion of (1 - 2x)^ | vedclass

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(B) The binomial expansion of $(1 + y)^n$ is $1 + ny + \frac{n(n-1)}{2!}y^2 + \frac{n(n-1)(n-2)}{3!}y^3 + \dots$Here,$n = \frac{3}{2}$ and $y = -2x$.T

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$\frac{x^3}{2}$

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(B) The binomial expansion of $(1 + y)^n$ is $1 + ny + \frac{n(n-1)}{2!}y^2 + \frac{n(n-1)(n-2)}{3!}y^3 + \dots$Here,$n = \frac{3}{2}$ and $y = -2x$.The $4^{th}$ term is given by the formula $T_4 = \frac{n(n-1)(n-2)}{3!}y^3$.Substituting the values:$T_4 = \frac{\frac{3}{2}(\frac{3}{2}-1)(\frac{3}{2}-2)}{3 	imes 2 	imes 1} (-2x)^3$$T_4 = \frac{\frac{3}{2} 	imes \frac{1}{2} 	imes (-\frac{1}{2})}{6} (-8x^3)$$T_4 = \frac{-\frac{3}{8}}{6} (-8x^3)$$T_4 = -\frac{3}{48} (-8x^3) = \frac{24}{48}x^3 = \frac{x^3}{2}$.

The fourth term in the expansion of $(1 - 2x)^{3/2}$ is:

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