Question

What is the 4th term of the quantity a minus the square root of 2 raised to the eighth power?

Answer 1

Let's see what the binomial theorem is telling us:

\[\Large (x+y)^n = \sum_{k=0}^n {n \choose k}x^{n-k}y^{k} \]

It says the sum of the exponents on x and y would be 8 since in this case n=8. And in this case \( x=a, y= -\sqrt 2 \).

So for the 1st term k=0. And in the 4th term k=3.