Factoring Quadratic
More Lessons for Algebra
Math Worksheets
In these lessons, we will learn how to factor quadratic equations that are the Perfect Square Trinomials (Square of a Sum or Square of a Difference) and Difference of Two Squares.
Related Topics:
Factoring Out Common Factors (GCF).
Factoring Quadratic Equations where the coefficient of x2 is 1.
Factoring Quadratic Equations where the coefficient of x2 is greater than 1
Factoring Quadratic Equations by Completing the Square
Factoring Quadratic Equations using the Quadratic Formula.
In some cases, recognizing some common patterns in the quadratic equation will help you
to factorize the quadratic. For example, the quadratic equation could be a Perfect Square Trinomial (Square of a Sum or Square of a Difference) or Difference of Two Squares.
Perfect Square Trinomial (Square Of a Sum)
A square of a sum or perfect square trinomial is a type of quadratic equations of the form:
x2 + 2bx + b2 = (x + b)2
| Example 1: | x2 + 2x + 1 = 0 |
| (x + 1)2 = 0 | |
 |
|
| Example 2: | x2 + 6x + 9 = 0 |
| x2 + 2(3)x + 32 = 0 | |
| (x + 3)2 = 0 | |
 |
Perfect Square Trinomial (Square of a Difference)
A square of difference is a type of quadratic equations of the form: x2 – 2bx + b2 = (x – b)2| Example 1: | x2 – 2x + 1 = 0 |
| (x – 1)2 = 0 | |
 |
|
| Example 2: | x2 – 6x + 9 = 0 |
| x2 – 2(3)x + 32 = 0 | |
| (x – 3)2 = 0 | |
| x – 3 = 0 ⇒ x = 3 |
This video provides examples of how to factor and solve quadratic equations when the equations are perfect square trinomials.
Perfect Square Trinomials
One special case when trying to factor polynomials is a perfect square trinomial. Unlike a difference of perfect squares, perfect square trinomials are the result of squaring a binomial. It's important to recognize the form of perfect square trinomials so that we can easily factor them without going through the steps of factoring trinomials, which can be very time consuming. Factor perfect square trinomialDifference of Two Squares
A difference of two squares is a type of quadratic equations of the form:
(a + b)(a – b) = a2 – b2
| Example: | x2 – 25 = 0 |
| x2 – 52 = 0 | |
| (x + 5)(x – 5) = 0 | |
| We get two values for x: | |
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Be careful! This method only works for difference of two squares and not for the sum of two squares: a2 + b2 ≠ (a + b)(a – b)
The following videos explain how to factor a difference of squares.Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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