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 $(1-2x{)}^{\frac{3}{2}}$

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

Hence $4^{th}$ term is $\frac{x^3}{2}$