Question

What is the coefficient for the third term in the expansion?

Answer 1

Answer:

2196

Step-by-step explanation:

3^2 = 9

9+3^7 = 2196

Answer 2

ANSWER

21

EXPLANATION

The given by binomial expression is:

$( {x}^{2} + y)^{7}$

Comparing this to

$(a+ b)^{n}$

We have:

$n = 7$

$a = {x}^{2}$

$b = y$

The coefficient of the (r+1)th term is given by:

$\binom{n}{r}$

We want to find the coefficient of the third term:

$r + 1 = 3$

$r = 2$

Therefore the coefficient is:

$\binom{7}{2} = 21$

The coefficient of the third term is 21.