Question

Please help! ASAP!!!

Answer 1

Final answer is
`-112\cdot√(2)a^5`.

Explanation:

Given expression is
`(a-√(2))^8`.

Now we need to find the fourth term of the given expression
`(a-√(2))^8`. So apply the nth term formula using binomial expansion.

exponent n=8

4th term means we use r=4-1=3

x=2,
`y=-√(2)`

rth term in expansion of
`(x+y)^n` is given by formula:

`(n!)/(\left(n-r\right)!\cdot r!)x^(\left(n-r\right))\cdot y^r`

`=(8!)/(\left(8-3\right)!\cdot3!)\cdot a^(\left(8-3\right))\cdot\left(-√(2)\right)^3`

`=(8!)/(5!\cdot3!)\cdot a^5\cdot\left(-2√(2)\right)`

`=(40320)/(120\cdot6)\cdot a^5\cdot\left(-2√(2)\right)`

`=56\cdot a^5\cdot\left(-2√(2)\right)`

`=-112a^5\cdot√(2)`

`=-112\cdot√(2)a^5`

Hence final answer is
`-112\cdot√(2)a^5`.