Introduction to Factorisation by Grouping
Factorisation by grouping is a method used in algebra to factorise expressions that cannot be factorised using simple factorisation methods. This method involves grouping terms together to create a common factor. In this article, we will explore the concept of factorisation by grouping, its application, and provide a comprehensive worksheet to help you practice.Understanding Factorisation by Grouping
Factorisation by grouping is a technique used to factorise expressions of the form ax + by + cx + dy, where a, b, c, and d are constants, and x and y are variables. The goal is to group the terms in such a way that we can extract a common factor from each group.Steps to Factorise by Grouping
To factorise an expression by grouping, follow these steps: * Group the terms into pairs, usually the first two terms and the last two terms. * Look for common factors within each group. * Extract the common factor from each group. * Factorise the remaining terms, if possible.Example of Factorisation by Grouping
Consider the expression: 2x + 4y + 3x + 6y To factorise this expression, we group the terms as follows: (2x + 4y) + (3x + 6y) Now, we look for common factors within each group: * 2x + 4y = 2(x + 2y) * 3x + 6y = 3(x + 2y) We can see that both groups have a common factor of (x + 2y). Therefore, the factorised form of the expression is: 2(x + 2y) + 3(x + 2y) = (2 + 3)(x + 2y) = 5(x + 2y)Worksheet: Factorisation by Grouping
Practice your skills with the following exercises:| Expression | Factorised Form |
|---|---|
| 3x + 6y + 2x + 4y | |
| 2x + 5y + x + 5y | |
| 4x + 8y + 3x + 6y | |
| x + 3y + 2x + 6y | |
| 5x + 10y + 2x + 4y |
📝 Note: When factorising by grouping, make sure to look for common factors within each group and extract them carefully to obtain the correct factorised form.
To solve these exercises, follow the steps outlined above and apply the concept of factorisation by grouping.
In summary, factorisation by grouping is a powerful technique for factorising complex algebraic expressions. By grouping terms together and extracting common factors, we can simplify expressions and make them easier to work with. With practice and patience, you can master this technique and become proficient in factorising a wide range of expressions.
What is factorisation by grouping?
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Factorisation by grouping is a method used in algebra to factorise expressions that cannot be factorised using simple factorisation methods. This method involves grouping terms together to create a common factor.
How do I factorise an expression by grouping?
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To factorise an expression by grouping, follow these steps: group the terms into pairs, look for common factors within each group, extract the common factor from each group, and factorise the remaining terms, if possible.
What are the benefits of factorisation by grouping?
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The benefits of factorisation by grouping include simplifying complex algebraic expressions, making them easier to work with, and providing a powerful technique for solving equations and inequalities.
How can I practice factorisation by grouping?
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You can practice factorisation by grouping by working through exercises and worksheets, such as the one provided above, and by applying the technique to real-world problems and applications.
What are some common mistakes to avoid when factorising by grouping?
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Common mistakes to avoid when factorising by grouping include failing to look for common factors within each group, extracting the wrong common factor, and not factorising the remaining terms correctly.