Question

Find the 4th term of the expansion

A
B
C
D

Answer 1

option-A

Explanation:

We can use rth term binomial expansion formula

`(x+y)^n`

`T_r=(n,r-1)x^(n-(r-1))y^(r-1)`

we are given

`(a-√(2))^8`

we can compare

`x=a,y=-√(2)`

n=8

r=4

now, we can find 4th term

`T_r=(8,4-1)a^(8-(4-1))(-√(2))^(4-1)`

now, we can simplify it

`T_4=(8!)/(5!3!)* -2√(2)a^5`

`T_4=56* -2√(2)a^5`

`T_4=-112√(2)a^5`

Answer 2

Option A.
`=-112a^(5)√(2)`

Explanation:

from the given formula of binomial
`(a+b)^(n)=a^(n)+na^(n-1)b+(n(n-1))/(2!)a^(n-2)b^(2)+(n(n-1)(n-2))/(3!)a^(n-3)b^(3).....b^(n)` we can calculate any term of this expansion.

Now from the question we have to find out the 4th term of
`(a-√(2) )^(8)`

From the expansion fourth term will be
`(n(n-1)(n-2))/(3!)a^(n-3)b^(3)`

Now we replace a=a, b=(-√2) and n=8

`(8(8-1)(8-2))/(3!)a^(8-3)(-√((2)))^(3)`

`= -(8* 7* 6)/(3* 2* 1)a^(5)(2)√(2)`
`=-8* 7a^5(2)√(2)`

`=-112a^(5)√(2)`