Question about a function

Question

I'd like to know how this f(x)=x^2-2px+p+6 can be simplified like this =(x-p)^2+p+6-p^2

Thanks!

Answer 1

f(x) = x² - 2px + p + 6

 

Add and subtract p² and get

 

f(x) = x² - 2px + p + 6 + p² - p² = (x² - 2px + p²) + p + 6 - p²

 

Note that 

 

x² - 2px + p² = (x - p)²

 

Then

 

f(x) = (x - p)² + p + 6 - p²