Question

The polynomial below is a perfect square trinomial of the form a2 - 2ab + b2

Answer 1

This is a true statement. Here's how we know. The factors of that general formula are (ax - b)(ax - b). If that is in fact the general formula of the quadratic shown, then our a would be 2 and our b would be 3, since 2 times 2 is 4 which is the leading coefficient, and 3 times 3 is 9 which is the constant. Those factors, filled in accordingly, would be (2x - 3)(2x - 3). If we FOIL those out we should get back the quadratic in question. FOILing gives us

$4x^2-6x-6x+9$

which of course simplifies to

$4x^2-12x+9$