Algebra: Factorisation By Grouping
In this video course, you will learn how to perform factorisation using the grouping method. Before starting, students should already be familiar with factorisation by common factor. Factorisation by grouping involves three techniques, and the appropriate technique is applied depending on the structure of the expression.
Related Lessons:
Direct Grouping Factorisation
In the direct grouping factorisation, we will factorise the first 2 terms and second 2 terms directly without any manipulation. Here are the steps:
Step 1: Factorise 2 terms by 2 terms by applying the Common Factors factorisation technique
Step 2: Factorise again the terms within the bracket
Step 3: Perform further factorisation (if required)
The second technique is changing position. We will need to apply this technique if we are uable to find any common factors between the first 2 terms or the second 2 terms. Here are the steps:
Step 1: Change the position of the terms since there are no common factors between the first two and last two terms.
- Swap the second and third term
- If the swapping fails, try swapping second and fourth term
Step 2: Perform factorisation, 2 terms by 2 terms
Step 3: Perform a second factorisation of the bracket term to get the answer
Step 1: Perform factorisation, 2 terms by 2 terms as per normal. We realise that the position of the terms inside the brackets have swapped.
Step 2: To make the terms within the two brackets to be the same:
- Change the external sign from positive to negative, or negative to positive
- Swap the position of the two terms inside the bracket
Step 3: Perform a second factorisation of the bracket term to get the answer