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D1. Elementary algebra : the product of linear expressions. Vocabulary Algebraic expressions like (x+1) or (x+2) are called linear. Any expression that can be written in the form ax+b, where a and b are numbers, is called a linear expression. Linear expressions can be multiplied together. This is often refered to as multiplying out brackets (or expanding brackets), for example, (x + 1)(x + 2)= x2 + 3x + 2 The resulting expression is called a quadratic function. All these functions are quadratic functions: x2 + 7x - 11, x2 - 12x , x2 + 14, 6x2+ x - 1, 5 - x2 Generally, quadratic functions have the form: ax2 + bx + c, where a, b and c are numbers and a ¹ 0 A method for multiplying out brackets can be illustrated by using a connection between multiplication and area. The total area of this rectangle represents (x+1)(x+2) Find the area of the first section. This area=x × x=x2 Now find the area of the second section. This area=x × 1=x Now the area of the third section. This area=2 × x=2x Finally find the area of the fourth section. This area=2 × 1=2 So the total area= x2 + x + 2x + 2=x2 + 3x + 2 This displays the process in a slightly different way: Practise multiplying out brackets. Choose your own value in the first two boxes. (x+ )(x+ )   x x x2 x x =  x2 + x +