What value of $k$ will make $x^2 - 16x + k$ the square of a binomial?
I know that the square of a binomial has the form $(x - a)^2 = x^2 - 2ax + a^2$. So I want to find a value of $k$ that makes $x^2 - 16x + k$ look like that. That means I need to have $-2a = -16$, or $a = 8$. Then I can plug in $a = 8$ into $a^2$ to get $k = 8^2 = 64$. To check, I can see that $x^2 - 16x + 64 = (x - 8)^2$, which is the square of a binomial.

