# What is the coefficient of the term x^6 in the expansion of (x+3)^10?

May 27, 2017

Coefficient of the term ${x}^{6}$ in the expansion of ${\left(x + 3\right)}^{10}$ is $17010$.

#### Explanation:

In the expanssion od ${\left(x + a\right)}^{n}$

${\left(r + 1\right)}^{t h}$ term is ${C}_{r}^{n} {x}^{n - r} {a}^{r}$

Hence in the expanssion of ${\left(x + 3\right)}^{10}$

${\left(r + 1\right)}^{t h}$ term is ${C}_{r}^{10} {x}^{10 - r} {3}^{r}$

As we need coefficient of ${x}^{6}$, we have $10 - r = 6$ or $r = 4$

and coefficient is ${C}_{4}^{10} {3}^{4}$

= $\frac{10 \cdot 9 \cdot 8 \cdot 7}{1 \cdot 2 \cdot 3 \cdot 4} \times 81 = 210 \times 81 = 17010$