Use Pascal's Triangle to expand the binomial.
\[
(8 v+s)^{5}
\]
(1 point)
$s^{5}+320 s^{4} v+5,120 s^{3} v^{2}+40,960 s^{2} v^{3}+16,380 s v^{4}+262,144 v^{5}$
$s^{5}-5 s^{4} v+10 s^{3} v^{2}-10 s^{2} v^{3}+5 s v^{4}-v^{5}$
$s^{5}+40 s^{4}+640 s^{3}+5,120 s^{2}+20,480 s+32,768$
$s^{5}+40 s^{4} v+640 s^{3} v^{2}+5,120 s^{2} v^{3}+20.480 s v^{4}+32,768 v^{5}$

Step 1 ：The question is asking to expand the binomial \((8v+s)^5\) using Pascal's Triangle. Pascal's Triangle is a triangular array of the binomial coefficients. The coefficients for the expansion of \((a+b)^n\) can be found in the nth row of Pascal's Triangle. The coefficients for the expansion of \((a+b)^5\) are 1, 5, 10, 10, 5, 1.

Step 2 ：The general form for the binomial expansion is \((a+b)^n = a^n + (n choose 1)a^(n-1)b + (n choose 2)a^(n-2)b^2 + ... + b^n\).

Step 3 ：So, to expand \((8v+s)^5\), we can substitute a=8v and b=s into the general form and calculate the terms.

Step 4 ：The expanded form of the binomial \((8v+s)^5\) is \(s^5 + 40s^4v + 640s^3v^2 + 5120s^2v^3 + 20480sv^4 + 32768v^5\). This matches with one of the options given in the question. So, I now know the final answer.

Step 5 ：Final Answer: The expanded form of the binomial \((8v+s)^5\) is \(\boxed{s^{5}+40 s^{4} v+640 s^{3} v^{2}+5,120 s^{2} v^{3}+20,480 s v^{4}+32,768 v^{5}}\)