What is Expansion?

A quadratic expression is an expression involving a squared term, e.g., x

2 + 1, or a product term, e.g., 3xy − 2x + 1. (A linear expression such as x + 1

is obviously non-quadratic.)

This is also known as the Distributive law, where 'a groups of b and c' is the same as 'a groups of c', i.e. 'a times of b' and 'a times of c' 

Example: 

2(x - 2) = 2x - 4

Using the distributing law, 2(x - 2) = '2 groups of (x - 2) 

 Therefore, 2(x - 2) = 2x - 4. 

Quadratic expressions can also come in the form of (a + b)(c + d) . 

(a + b)(c + d) = a(c + d) + b(c + d) 

                    = ac + ad + bc + bd 

Example: 

(x + 4)(x + 5) = x(x + 5) + 4(x + 5)         (multiply the expression in the second bracket by each                                                                                term in the first bracket) 

                     = x² + 5x + 4x + 20            (Distributive law) 

                     = x² + 9x + 20                   (group like terms)