Mathematics: What is the fourth term of (x + y)8

What is the fourth term of (x + y)8

Ответ:

aaliyahettorre

08.01.2022

Mathematics

The required forth term of the given expansion is 56x^5y^3.

Step-by-step explanation: We are given to find the fourth term of the following binomial expansion :

E=(x+y)^8.

We know that

in the binomial expansion of the expression (a+b)^n , the r-th term is given by

$T_r=^nC_{r-1}a^{n-r+1}b^{r-1}.$

Therefore, the fourth term of the given binomial expansion will be

$T_4\\\\\\=^8C_{4-1}x^{8-4+1}y^{4-1}\\\\\\=\dfrac{8!}{3!(8-3)!}x^5y^3\\\\\\=\dfrac{8\times7\times6\times5!}{3\times2\times1\times5!}x^5y^3\\\\\\=56x^5y^3.$

Thus, the required forth term of the given binomial expansion is 56x^5y^3.

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What is the fourth term of (x + y)8

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