Question

Find the coefficient of $x^8{y}^{12}$ in the expansion of $(x+2y{)}^{20}$

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$(r+1{)}^{th}$ term or $T_{r+1}$ in the expansion of $(x+2y{)}^{20}is{}^{20}{C}_r{x}^{20-r}(2y{)}^r$
or ${}^{20}{C}_r{2}^r{x}^{20-r}{y}^r$
$x^8{y}^{12}\equiv x^{20-r}{y}^r$
$\Rightarrow$ r=12
$\Rightarrow$ Coefficient of $x^8{y}^{12}={}^{20}{C}_{12}{2}^{12}$