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) × (ab) = a2b2

     

    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

     

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