Algebraic Manipulation

 

 

 

Contents

 

Simple Algebraic Expressions

 

Evaluation of Algebraic Expression

 

Rules of Algebra

 

Algebraic Fractions

 

Quiz 1

 

Expansion: The Foil Method

 

Algebraic Identities

 

Basic Factorisation

 

Factorisation of Quadratic Polynomials

 

Factorisation by Grouping

 

Quiz 2

 

Long Division

 

Polynomial Identities

 

Quiz 3

 

 

Algebra Main Page

Rules of Algebra

In algebra, terms of the same kind (called like terms) can be added or subtracted from one another.

Example:

a + a = 2a

2a + 5b + 4a + 8b= (2a + 4a) +(5b + 8b) = 6a +13b

7b - 3b= 4b

9c + 7d - 4c - 5d = (9c - 4c) + (7d - 5d) = 5c + 2d 

 
In multiplication and division, the coefficient and the variable are multiplied or divided. 
Example:

3 x 6a = 3 x 6 x a = 18 x a = 18a
 
 

In simplifying algebraic expressions, we also use the distributive law to help us to 'remove the bracket'.
 
Example:
 
a(b + c) = a x b + a x c = ab +ac
 
-2a(b - c) = -2ab + 2ac  
 
(5s + 3t)4d = 5s x 4d + 3t x 4d = 20sf +12td
 
5e -(f + 6g)= 5e - f - 6g