ANSWER
21
EXPLANATION
The given by binomial expression is:
[tex]( {x}^{2} + y)^{7} [/tex]
Comparing this to
[tex](a+ b)^{n} [/tex]
We have:
[tex]n = 7[/tex]
[tex]a = {x}^{2} [/tex]
[tex]b = y[/tex]
The coefficient of the (r+1)th term is given by:
[tex] \binom{n}{r} [/tex]
We want to find the coefficient of the third term:
[tex]r + 1 = 3[/tex]
[tex]r = 2[/tex]
Therefore the coefficient is:
[tex]\binom{7}{2} = 21[/tex]
The coefficient of the third term is 21.
