Perfect square trinomial

Definition

A perfect square trinomial is a quadratic expression that can be written as the square of a binomial. It takes the form $a^2 + 2ab + b^2 = (a + b)^2$ or $a^2 - 2ab + b^2 = (a - b)^2$.

5 Must Know Facts For Your Next Test

1. Identifying a perfect square trinomial involves recognizing it matches either $(a+b)^2$ or $(a-b)^2$ forms.
2. The middle term in a perfect square trinomial is always twice the product of the square roots of the first and last terms.
3. Factoring perfect square trinomials simplifies solving quadratic equations and understanding polynomial identities.
4. Completing the square technique often uses perfect square trinomials to solve quadratic equations.
5. Perfect square trinomials are always positive or zero since they result from squaring binomials.

Review Questions

• What is the factored form of $x^2 + 10x + 25$?
• How do you recognize a perfect square trinomial in an equation?
• Explain why $4x^2 -12x +9$ is considered a perfect square trinomial.

Related terms

Binomial:

An algebraic expression containing two distinct terms, such as $a+b$.

Quadratic Equation:

A second-order polynomial equation in one variable, generally expressed as $ax^2+bx+c=0$.

Completing the Square:

\text{A method used to solve quadratic equations by converting them into a perfect square trinomial.}