What Are Perfect Square Trinomials?

What Are Perfect Square Trinomials?

A perfect square trinomial is a polynomial with three terms that is expanded or FOILed form of a binomial squared. Taking the square root of a perfect square trinomial will result in a rational expression, unlike the roots of other trinomials.

A polynomial is a mathematical expression with multiple terms that usually cannot be simplified or combined anymore than they are. Trinomials have three terms. These terms frequently include one or more variables that are either different themselves or raised to different powers.

x^2 + 6x + 9 is a trinomial, because it has three terms, none of which can be combined. It is also a perfect square.

Perfect square trinomials follow the rule that a^2 + 2ab + b^2 = (a + b)^2. Therefore, x^2 + 6x + 9 must equal (x + 3)^2. (x + 3)*(x + 3) can be expanded using a method called FOIL, which stands for first, outside, inside, last.

The square of the first term is x^2 because x*x = x^2. The product of the inside terms and that of outside terms can be added together: 3x + 3x = 6x. The square of the last term is 9 because 3*3 = 9.

To factor perfect-square trinomials, students determine the square roots of the outside and inside terms. If twice the product of their square roots is the middle term, then the original trinomial is a perfect square.