Answer:
Option d. [tex]126x^5y^4[/tex].
Step-by-step explanation:
Based on binomial theorem we write down the binomial formula for all positive integer values of n as-
[tex](a+b)^{n}=a^{n}+na^{n-1}b+\frac{n(n-1)}{2!}a^{n-2}b^{2}+\frac{n(n-1)(n-2)}{3!}a^{n-3}b^{3}.....b^{n}[/tex]
Now we calculate the 5th term of [tex](x+y)^{n}[/tex]
From the given formula the fifth term of the binomial will be
= [tex]\frac{n(n-1)(n-2)(n-3)}{4!}x^{n-4}y^{4}[/tex]
Here the value of n = 9
Then the fifth term will be[tex]=\frac{9(9-1)(9-2)(9-3)}{4!}x^{9-4}y^{4}[/tex]
[tex]=\frac{9(8)(7)(6)}{4!}x^{5}y^{4}=\frac{9\times 8\times 7\times 6}{4\times 3\times 2\times 1}x^5y^4[/tex]
[tex]=9\times 2\times 7x^5y^4=126x^5y^4[/tex]
