Question

question 5 of 10
what is the coefficient of ( x^3 y^2 ) in the expansion of ( (2x + y)^5 )?

a. 2

b. 5

c. 40

d. 80

e. it does not exist.

Explanation:

Step1: Recall binomial theorem

The general term of $(a+b)^n$ is $\binom{n}{k}a^{n-k}b^k$.

Step2: Identify values for the term

For $x^3y^2$ in $(2x+y)^5$, $n=5$, $k=2$ (since $y^2$), $a=2x$, $b=y$.

Step3: Calculate the coefficient

$\binom{5}{2}(2x)^{3}y^{2} = 10 \times 8x^3y^2 = 80x^3y^2$.

Answer:

D. 80