Business Mathematics

CHAPTER 2

Algebra

2.1  ALGEBRA

It is a branch of Mathematics that uses alphabets in place of unknown values.

Note: The alphabet may be a constant (fixed value) or a variable (non-fixed value).

EXAMPLE

Find the area of a rectangle with width w and height h.

Area = width × height; A = w × h

Here w and h are referred to as variables.

Specifically, if w = 10 cm and h = 6 cm, then the area is defined as

 

A = w × h = 10 × 6 = 60 cm²

2.2  ALGEBRAIC IDENTITIES

An algebraic identity is a relation that is true for all possible values of the literal symbols occurring in it.

EXAMPLES

1.  

   (a + b) × (a − b) = a² − b²

    

   The above identity is true for all real values of a and b.

   If a = 5 and b = 3

    

   (5 + 3) × (5 − 3) = 8 × 2 = 16; 5² − 3² = 25 − 9 = 16