Question

Find the coefficient of third term of (x + 2)³. A. 40 OB. 10 OC. 20 D. 80 Reset Selection A

Answer 1

Given:

The expression given is,

$\left(x+2\right)^5$

Required:

To find the coefficient of the third term.

Explanation:

Let us expand the expression to find the coefficient.

$\begin{gathered} \left(x+2\right)^5 \\ =\frac{5!}{5!}x^52^0+\frac{5!}{4!}x^42^1+\frac{5!}{2!3!}x^32^2+\frac{5!}{3!2!}x^22^3+\frac{5!}{4!1!}x^12^4+\frac{5!}{5!0!}x^02^5 \\ =x^5+10x^4+40x^3+80x^2+80x+32 \end{gathered}$

Hence, the coefficient of the third term is 40.

Final Answer:

The coefficient of the third term is 40.

Option A is correct.