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

Expansion: The Foil Method

For example, you are given the question: (20+3) (40+5). The fastest way is to first add, then multiply in the usual way :  23 x 45. Suppose that you can't add first, could you still solve the problem?

Easy, just follow the method below.

 
Use the same logic to work this problem.
 
This method is known as the FOIL method.
 
Example 1:
 
(2h - 5k) (2z + 5y)
      
   =4hz +10kz +25ky +10hy
 
 
Example 2:
 
(a2 -3a + 4) (a - 3)
   
   = a3 - 3a2 + 4a - 3a2 + 9a - 12 
   = a 3 + 6a2 + 13a - 12a
 

Example 3:

(3 - 2y) (y +1) (6 - y)

   = (3y +3 - 2y2 - 2y) (6 - y)

   = (-2y2 + y + 3) (6 - y)
   = -12y2 + 6y + 18 + 2y3 - y2 - 3y
   = 2y3 -13y2 +3y +18