Complete the square on:
x^2 - 8k
k^2 + 4k
Isn't it k^2 - 8k in the first one ?
You must associate these expressions with the formulas you should know :
(a-b)² = a² - 2ab + b²
(a+b)² = a² + 2ab + b²
So in each case, you'll got to find what is a. Then find 2ab. Hence, you got b, and you complete your expressions with b²
We are comparing this to
So by matching the coefficients of the linear (k) term we see that
Thus we need to add to the expression. But we can't do that and not change the expression. So we have to be a bit clever about this and add to the expression. That way the value of the expression does not change.
You do the second one.