Factor $d^k+(a-d)^k$ I was reading a number theory book and it was stated that $d^k+(a-d)^k=a[d^{k-1}-d^{k-2}(a-d)+ . . .+(a-d)^{k-1}]$ for $k$ odd. How did they arrive at this factorization? Is there an easy way to see it?

Start by understanding how to factor
$$
x^n - y^n .
$$
Presumably you know how to do that when $n=2$. For $n=3$ you can check that
$$
x^3 - y^3  = (x-y)(x^2 + xy + y^2)
$$
Now guess for higher powers.
Then see what happens if $n$ is odd and you replace $y$ by  $(-y)$.
