How do you identify perfect square trinomials and differences of square binomials for factoring?

A perfect square is a number that can be expressed as the product of two equal integers. To determine that a trinomial is a perfect square we use the the discriminant given by:

b^2-4ac

where a, b and c have been obtained from the trinomial given by:

ax^2+bx+c;

if the value of the discriminant is a perfect square then the trinomial is a perfect square trinomial