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