Question

The coefficient of $c^2{d}^2$ in the expansion of $(\sqrt{c}+\sqrt{d}{)}^8$, is

• A. 28
• B. 45
• C. 56
• D. 70

Answer 1

Answer: (D)

$(\sqrt{c}+\sqrt{d}{)}^8;{}^8{C}_r{c}^{\frac{8-r}{2}}{d}^{\frac{r}{2}}\Rightarrow r=4$
$\text{ coefficient }={}^8{C}_4=\frac{8\times 7\times 6\times 5}{24}=70.$