Question

How do you factor completely: `x^2 +4x +4`?

Answer 1

We know: `(x + y)^2 = x^2 + 2xy + y^2` (Memorise)
Thus, we have: `x^2 + 4x + 4 = x^2 + 2(2)x + 2^2 = (x + 2)^2`

You can also read this article on Wikipedia:
https://en.wikipedia.org/wiki/Completing_the_square
Watch the animation in the page to get a good intuition of the formula.