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 \(56x^5y^3.\)
