Factorisation by Regrouping Terms Factorisation involves writing a number as a product of two or more smaller numbers in a simpler form. Grouping terms toget...
Factorisation involves writing a number as a product of two or more smaller numbers in a simpler form. Grouping terms together through factorisation allows for easier identification of those factors.
Key Concept: By regrouping terms, we rewrite the expression in a more convenient way, revealing the factors of the original number.
Regrouping: Group similar terms together based on their numerical characteristics.
Steps in Factorisation by Regrouping:
Identify the largest factors: Start by finding the largest numbers or variables that evenly divide the original number. These are the main factors of that number.
Group like terms: Group together terms with the same numerical characteristics, such as factors with the same prime factor or factors with the same degree.
Combine like terms: Combine terms with the same factor together, regardless of their position.
Write the expression using factors: Once the groups are formed, write the original expression as a product of the groups, using each group as a factor.
Check the result: Check if the simplified expression matches the original number. If it does, you have successfully factorised the original expression.
Examples:
Factor 12 = 2 x 2 x 3 x 3: Here, the largest factors are 2, 2, 3, and 3, and the terms can be grouped as 2^2 * 3^2.
Factor 15 = 3 x 5: This is a simple case of grouping like terms together.
Benefits of Factorisation by Regrouping:
Identifies factors: It helps you identify the individual factors of the original number by combining like terms.
Makes expressions simpler: By grouping terms, the expression becomes more concise and easier to understand.
Provides visual insight: The grouping process creates a visual representation of the factors, aiding in understanding the factors and their relationships.
Practice:
Apply the steps above to factorise the following numbers:
30
60
90
120