Question

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

Answer 1

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)\\\\\\=(8!)/(3!(8-3)!)x^5y^3\\\\\\=(8*7*6*5!)/(3*2*1*5!)x^5y^3\\\\\\=56x^5y^3.`

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

Answer 2

(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)`