Question

The fourth term in the expansion of $(1-2x{)}^{\frac{3}{2}}$ will be

• A. $-\frac{3}{4}{x}^4$
• B. $\frac{x^3}{2}$
• C. $-\frac{x^3}{2}$
• D. $\frac{3}{4}{x}^4$

Answer 1

The correct option is B $\frac{x^3}{2}$

Expansion of $(1-2x{)}^{3/2}$ would be

$1-\frac{3}{2}\left(2n\right)+\frac{\frac{3}{2}(\frac{3}{2}-1)}{2}(2x{)}^2-\frac{\frac{3}{2}(\frac{3}{2}-1)(\frac{3}{2}-2)}{6}(2x{)}^3$

$\Rightarrow$ Forth term $=\frac{\frac{3}{2}\left(\frac{1}{2}\right)\left(\frac{-1}{2}\right)}{6}\left(3x^3\right)=\frac{1}{2}{x}^3\Rightarrow \left(B\right)$