When deriving the quadratic formula by completing the square, what expression can be added to both sides of the equation to create a perfect square trinomial?

According to steps 2 and 4. The second-order polynomial must be added by and to create a perfect square trinomial.

Step-by-step explanation:

Let consider a second-order polynomial of the form , . The procedure is presented below:

1) (Given)

2) (Compatibility with addition/Existence of additive inverse/Modulative property)

3) (Compatibility with multiplication)

4) (Compatibility with addition/Existence of additive inverse/Modulative property)

5) (Perfect square trinomial)

According to steps 2 and 4. The second-order polynomial must be added by and to create a perfect square trinomial.