Mathematics: Find the 5th term of the expansion of (x + y)^9 a. 81x4y5 c. 81x5y4 b. 126x4y5 d. 126x5y4 select the best answer from the choices provided a b c d

sorry i can not helpStep-by-step explanation:...

Find the 5th term of the expansion of (x + y)^9

kprincess16r

09.03.2022

Option d. 126x^5y^4 .

Step-by-step explanation:

Based on binomial theorem we write down the binomial formula for all positive integer values of n as-

$(a+b)^{n}=a^{n}+na^{n-1}b+\frac{n(n-1)}{2!}a^{n-2}b^{2}+\frac{n(n-1)(n-2)}{3!}a^{n-3}b^{3}.....b^{n}$

Now we calculate the 5th term of $(x+y)^{n}$

From the given formula the fifth term of the binomial will be

= $\frac{n(n-1)(n-2)(n-3)}{4!}x^{n-4}y^{4}$

Here the value of n = 9

Then the fifth term will be $=\frac{9(9-1)(9-2)(9-3)}{4!}x^{9-4}y^{4}$

$=\frac{9(8)(7)(6)}{4!}x^{5}y^{4}=\frac{9\times 8\times 7\times 6}{4\times 3\times 2\times 1}x^5y^4$

$=9\times 2\times 7x^5y^4=126x^5y^4$

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