Factoring - Algebra

Factoring is the reverse process of special product but it is harder to analyse especially if the given has big values. It is an essential part of algebra because it is used for simplifying expressions and functions.

* Types of Factoring

1. Common Monomial Factor

            - Separation of the common variable or numerical coefficient from two or more monomials in an expression.

Formula:

ax + ay = a(x + y)

Examples:

* 2x - 6y = 2(x - 3y)

* x³ + 2x² - x = x(x² + 2x - 1)

2. Difference of Two Squares

Formula:

x² - y² = (x + y)(x - y)

Examples:

* 9x² - 81 = (3x + 9)(3x - 9)

* 25a⁴ - 1 = (5a² +1)(5a² - 1)

3. Perfect Square Trinomial

Formula:

x² + 2xy + y² = (x + y)²
x² - 2xy + y² = (x - y)²

Examples: 

* 25x² - 40x + 16 = (5x - 4)²

* 100x⁴ + 100x² + 25 = (10x² + 5)²

4. Sum and Difference of Two Cubes

Formula: 

x³ + y³ = (x + y)(x² - xy + y²)
x³ - y³ = (x - y)(x² + xy + y²)

Examples:

* 8x³ - 1 = (2x)³ - 1³

= (2x - 1)(4x² + 2x + 1)

* 27x⁹ + 8 = (3x³)³ + (2)³

= (3x³ + 2)(9x⁶ - 6x³ + 4)

* Factoring in Simplifying an Expression

Examples: