help please!

Question

1. How is the factoring of perfect square trinomials and differences of squares connected to the factoring of simple and/or complex trinomials?

Answer 1

Take the trinomial a²±2ab+b² and a²-b².

These can be written (a±b)² and (a-b)(a+b).

So the square root of the perfect square trinomial is a±b, therefore a+b or a-b is always a factor of the difference of the same two squares a and b.