Question

Find the coefficient of $x^6{y}^3$ in the expansion of $(x+2y{)}^9$.

• A. $674$
• B. $670$
• C. $676$
• D. $672$

Answer 1

Answer: (D)

Let $x^6{y}^3$ be the $(r+1{)}^{th}$ term in the expansion of $(x+2y{)}^9$.
Now $T_{r+1}={}^9{C}_r{x}^{9-r}{\left(2y\right)}^r$
$={}^9{C}_r{2}^r\cdot x^{9-r}\cdot y^r$.
Comparing the indices of $x$ and $y$ in $x^6{y}^3$ and in $T_{r+1}$, we get $r=3$.
Thus, the coefficient of $x^6{y}^3={}^9{C}_3{2}^3=672$.