Perfect square trinomial

Definition

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial. It takes the form $a^2 + 2ab + b^2$ or $a^2 - 2ab + b^2$.

5 Must Know Facts For Your Next Test

1. A perfect square trinomial always factors into $(a+b)^2$ or $(a-b)^2$.
2. The middle term in $a^2 + 2ab + b^2$ is twice the product of the square roots of the first and last terms.
3. It is crucial to recognize perfect square trinomials for simplifying expressions and solving equations.
4. Perfect squares are useful in completing the square method for solving quadratic equations.
5. Identifying a perfect square trinomial helps in graphing parabolas since it simplifies finding vertex form.

Review Questions

• What is the factored form of the perfect square trinomial $x^2 + 6x + 9$?
• Identify whether $4x^2 - 12x + 9$ is a perfect square trinomial and, if so, factor it.
• What are the characteristics that define a perfect square trinomial?

Related terms

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

Quadratic Equation: An equation of the form $ax^2+bx+c=0$, where $a$, $b$, and $c$ are constants.

Completing the Square: A method used to solve quadratic equations by transforming them into a perfect square trinomial.