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 x^{2 }is 1.
Factoring Quadratic Equations where the coefficient of x^{2} 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.
A square of a sum or perfect square trinomial is a type of quadratic equations of the form:
x^{2} + 2bx + b^{2} = (x + b)^{2}
Example 1: | x^{2} + 2x + 1 = 0 |
(x + 1)^{2} = 0 | |
Example 2: | x^{2} + 6x + 9 = 0 |
x^{2} + 2(3)x + 3^{2} = 0 | |
(x + 3)^{2} = 0 | |
A square of difference is a type of quadratic equations of the form: x^{2} – 2bx + b^{2} = (x – b)^{2}
Example 1: | x^{2} – 2x + 1 = 0 |
(x – 1)^{2} = 0 | |
Example 2: | x^{2} – 6x + 9 = 0 |
x^{2} – 2(3)x + 3^{2} = 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.
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 trinomial
A difference of two squares is a type of quadratic equations of the form:
(a + b)(a – b) = a^{2} – b^{2}
Example: | x^{2} – 25 = 0 |
x^{2} – 5^{2} = 0 | |
(x + 5)(x – 5) = 0 | |
We get two values for x: | |
The following videos explain how to factor a difference of squares.
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