Factorisation

Factorisation is the process of expressing an algebraic expression as a product of its factors.
1.       Factorisation by a common factor

Example 1:

       5x + 15 = 5( x + 3)

As 5 and 15 have the common factor of 5, you can factor the out the 5, and place it in front of the bracket. There, you get your answer of 5(x+3)

 

2. Special identities

a² + 2ab +b²= (a+b)²

a² - 2ab +b² = (a-b)²

a² + b² = (a+b)(a-b)

Example 2:

x²+ 12x + 36 = (a + b) ²                                               a = x

                   = (x + 6) ²                                               b = 6

 

Note:  both ‘x²’ and ‘36’ have to be perfect squares, and the highlighted sign has to be a positive sign.

3. Cross method

x² + x – 2 = ( x + 2)(x – 1)

 

In the first 2 columns, the two rows must be multiplied and the product should be what is in the third row. After that, cross multiply as seen in the picture, and add the two products together in the third column, third row.  Your answers are in the two brackets.

4. Grouping

Xy+ 4x + 3y + 12 = (xy + 4x) + (3y +12)

                           =x(y + 4) + 3(y + 4)

              =(y + 4)(x + 3)

Group them into two groups with the same factors, and factorise the common factor outside the brackets. The common factor outside both brackets will then be grouped together in a bracket. There, you get your answer.