Factoring Quadratic

In some cases recognizing some common patterns in the quadratic equation will help you to factorize the quadratic.

For example: Square of Sum, Square of Difference and Difference of Two Squares

Square Of Sum

A square of sum 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

Square of 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

Difference 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:

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)

Videos

The following videos explain how to factor a difference of squares.

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.

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