A perfect square trinomial is the square of a binomial. It follows a pattern when it is factored, so that the first and last terms are perfect squares of monomials and the middle term is twice their product. If the pattern does not fit for a particular trinomial, it is not a perfect square trinomial.
The process for squaring a binomial is the same. Suppose the binomial were x-4 instead. Squaring the binomial x-4 is the same thing as multiplying x-4 x For this:.
Before we can get to defining a perfect square, we need to review some vocabulary. Perfect squares are numbers or expressions that are the product of a number or expression multiplied to itself. Perfect square trinomials are algebraic expressions with three terms that are created by multiplying a binomial to itself.
Recognizing when you have these perfect square trinomials will make factoring them much simpler. They are also very helpful when solving and graphing certain kinds of equations. We're now trying to see if we can get the middle term of 2 a b 2ab 2 ab. You've solved a perfect square trinomial!
You're now ready to apply trinomial factoring to some practice problems. We know that this is a perfect square, and all we're asked is to factor it. Therefore, just take a look at the first and last term and find what they are squares of.
It'll give us:. Take out the common factor 3 3 3. Then times 2 2 2 :. To double check your answers, this online calculator will help you factor a polynomial expression.
Use it as a reference, but make sure you learn how to properly go through the steps to answering a perfect square trinomial question. Wasn't quite sure on the concepts covered in this chapter?
Perhaps you may want to go back and review how to find common factors of polynomials or how to factor by grouping. Also read up on solving polynomials with unknown coefficients, and the intro to factoring polynomials.
Ready to move on? Up next, learn how to complete the square and change a quadratic function from standard form to vertex form. Back to Course Index. Perfect Square Trinomial Pattern 3. How to Factor a Perfect Square Trinomial?
Perfect Square Trinomial Formula 5. Great learning in high school using simple cues. Indulging in rote learning, you are likely to forget concepts. With Cuemath, you will learn visually and be surprised by the outcomes. Practice Questions on Perfect Square Trinomial. Explore math program. Explore coding program.
Worksheet on Perfect Square Trinomial. Make your child naturally math minded.
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