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D1. Elementary algebra
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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.

This example shows you how to multiply out (x+1)(x+2)
The total area of this rectangle represents (x+1)(x+2) brackets Find the area of the first section. This area=x × x=x² brackets
       
Now find the area of the second section. This area=x × 1=x brackets Now the area of the third section. This area=2 × x=2x brackets
       
Finally find the area of the fourth section. This area=2 × 1=2 brackets So the total area =
x² + x + 2x + 2 = x² + 3x + 2

Therefore (x+1)(x+2) = x² + 3x + 2

Now follow the steps in mutliplying out for a number of different examples:


Practise your skill of multiplying out brackets. Click on "Multiply out" to get started. Try to get 10 correct answers at least before you move on.
(x+ )(x+ )
x
x
x²
x
x

=  x² + x +

Coded:
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