Question

Please help! ASAP!!!

Answer 1

Answer:

Final answer is $-112\cdot\sqrt{2}a^5$.

Step-by-step explanation:

Given expression is $(a-\sqrt{2})^8$.

Now we need to find the fourth term of the given expression  $(a-\sqrt{2})^8$. So apply the nth term formula using binomial expansion.

exponent n=8

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

x=2, $y=-\sqrt{2}$

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

$\frac{n!}{\left(n-r\right)!\cdot r!}x^{\left(n-r\right)}\cdot y^r$

$=\frac{8!}{\left(8-3\right)!\cdot3!}\cdot a^{\left(8-3\right)}\cdot\left(-\sqrt{2}\right)^3$

$=\frac{8!}{5!\cdot3!}\cdot a^5\cdot\left(-2\sqrt{2}\right)$

$=\frac{40320}{120\cdot6}\cdot a^5\cdot\left(-2\sqrt{2}\right)$

$=56\cdot a^5\cdot\left(-2\sqrt{2}\right)$

$=-112a^5\cdot\sqrt{2}$

$=-112\cdot\sqrt{2}a^5$

Hence final answer is $-112\cdot\sqrt{2}a^5$.