Question

What is the difference between perfect square trinomials and the difference of two squares?

Answer 1

Perfect square trinomials:

\(a^2 + 2ab + b^2 = (a + b)^2 \)
\(a^2 - 2ab + b^2 = (a - b)^2 \)

Difference of two squares:

\(a^2 - b^2 = (a + b)(a - b) \)

The square of a binomial results in a trinomial. That is the perfect square trinomial.
The product of a sum and a difference results in a the difference of squares which is a binomial.