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 | |
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 |
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: | |
Be careful! This method only works for difference of two squares and not for the sum of two squares: a^{2} + b^{2} ≠ (a + b)(a – b)
The following videos explain how to factor a difference of squares.