Perfect Square Trinomial

Definition

A perfect square trinomial is a quadratic expression that can be factored into a binomial square. It is a trinomial of the form:

a^2 + 2ab + b^2

or

a^2 -2ab + b^2

where a and b are real numbers. 

In simpler terms, a perfect square trinomial is the result of squaring a binomial. The general factorization is:

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

or

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

Example 1:

x^2 + 6x + 9

This is a perfect square trinomial because it factors as:

(x + 3)^2

Example 2:

x^2 -8x + 16

This is also a perfect square trinomial because it factors as:

(x - 4)^2

In summary, a perfect square trinomial is a quadratic expression that can be factored into the square of a binomial.