Question

The coefficient of term that contains $x^{10}{y}^3{z}^2$ in the expansion of the binomial ${(x^2-2y+z)}^{10}$ is

• A. $-\frac{8.\left(10\right)!}{2!.3!.5!}$
• B. $\frac{8.\left(10\right)!}{2!.3!.5!}$
• C. $\frac{\left(10\right)!}{2!.3!.5!}$
• D. $-\frac{\left(10\right)!}{2!.3!.5!}$

Answer 1

The correct option is A $-\frac{8.\left(10\right)!}{2!.3!.5!}$

The term $a^{r_1}{b}^{r_2}{c}^{r_3}$ in $(a+b+c{)}^n$ is $\frac{n!}{r_1!r_2!r_3!}\left(a{)}^{r_1}\right(b{)}^{r_2}(c{)}^{r_3}$

The term Coefficient of $x^{10}{y}^3{z}^2$ in $(x^2-2y+z{)}^{10}$is $\frac{10!}{5!3!2!}\left(1{)}^5\right(-2{)}^3(1{)}^2=\frac{-8\left(10\right)!}{2!3!5!}$