Question

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

Answer 1

(x+y$)^{2}$
The fourth term is;
$x^{5} (y )^{3}$
=$x^{5} y^{3}$
From table of binomial coefficients;
=56$x^{5} y^{3}$

Answer 2

Answer:  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 $56x^5y^3.$