Factorising double brackets is a crucial skill in algebra, often proving a stumbling block for many students. But don't worry! Mastering this technique is easier than you think with the right approach and a little practice. This guide provides simple tips and strategies to help you confidently factorise expressions into double brackets.
Understanding the Basics: What is Factorising?
Before diving into double brackets, let's clarify what factorising means. Essentially, it's the reverse of expanding brackets. When you expand brackets, you multiply; when you factorise, you find the common factors and rewrite the expression as a product. For example, expanding (x + 2)(x + 3) gives you x² + 5x + 6. Factorising x² + 5x + 6 reverses this process, returning you to (x + 2)(x + 3).
Breaking Down Double Brackets Factorisation
Factorising quadratic expressions (expressions with x²) into double brackets typically involves finding two numbers that add up to the coefficient of the 'x' term and multiply to the constant term.
Let's illustrate with an example:
Factorise x² + 7x + 12
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Identify the coefficients: The coefficient of x is 7, and the constant term is 12.
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Find two numbers: We need two numbers that add up to 7 and multiply to 12. Those numbers are 3 and 4 (3 + 4 = 7 and 3 * 4 = 12).
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Write the factorised form: The factorised form is (x + 3)(x + 4).
Always check your answer! Expand your factorised brackets to ensure you get back to the original expression.
Tackling More Complex Examples
Sometimes, the numbers aren't as straightforward. Let's look at a slightly more challenging example:
Factorise 2x² + 11x + 12
This example introduces a coefficient for the x² term. This adds a layer of complexity, requiring a slightly different approach:
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Identify the coefficients: The coefficient of x² is 2, the coefficient of x is 11, and the constant term is 12.
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Find factors: We need to find two numbers that multiply to (2 * 12) = 24 and add up to 11. These numbers are 3 and 8.
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Rewrite and simplify: Rewrite the original expression: 2x² + 3x + 8x + 12. Then factorise by grouping: x(2x + 3) + 4(2x + 3). Notice the common factor (2x + 3).
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Final Factorised Form: (2x + 3)(x + 4)
Practice Makes Perfect
The key to mastering factorising double brackets is consistent practice. Work through various examples, starting with simpler ones and gradually increasing the difficulty. Use online resources, textbooks, or worksheets to find plenty of practice problems. The more you practice, the quicker and more confident you'll become.
Useful Resources
While I cannot provide direct links to download materials, I encourage you to search online for "factorising quadratic expressions practice worksheets" or "factorising double brackets exercises" to find numerous resources to help you hone your skills. Many educational websites offer free practice exercises and tutorials.
By following these simple tips and dedicating time to practice, you'll confidently conquer factorising double brackets and build a solid foundation in algebra. Remember, consistent effort is the key to success!
