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

Basic Factorisation

We can use the expand the product a(b+c) to ab+ ac. Conversely, we can write ab+ ac as a(b+c). This process is known as factorisation. Factorisation is the opposite of expansion.

In factorisation, you will have to find the highest common factor. Once it is found, you can use the Distributive Law to write the polynomial in factored form.

 

5y³ +15y²

 

  = 5y² (y +3)

 

There are two special factorisations. We will take a look at perfect squares first. 

 

For example, 16y² + 8y + 1 = (4y+1)² 

 

Tip: Though the first and last terms are perfect squares, the middle term must be double the product of the square roots for the expression to be a perfect square.

 

Example 1:

 

36y² - 84y + 49

      

   =(6y² -7)²

 

Example 2:

 

9a² +30a + 25

   

   = (3a + 5 )² 

   

Another special factorisation is differences of two squares.

For example, 4y - 49 = (2y +7) (2y - 7)²

Tip: If there is no middle product in the differences of two squares, the operations in the binominal factors must be opposite. 

Example :

49c² - d²e² 

   = (7c + de) (7c -de)