Ever wondered why algebra seems to follow patterns everywhere? Quadratics...
Maths1,138 views·Updated 7 Sept 2026·2 pagesMastering Quadratics: Knowledge Organizer for GCSE AQA
L
Luck@imbored2999
1
of 2
Expanding and Factorising Quadratics
Think of expanding brackets like unpacking a suitcase - you're taking everything out and spreading it around. When you see something like 4, multiply the 4 by everything inside those brackets to get 4a + 24.
Factorising works the opposite way - you're packing things back into the suitcase by finding the Highest Common Factor (HCF). For example, 4x + 12 becomes 4 because 4 divides into both terms perfectly.
The real fun starts with double brackets like x-5$$x+2. You need to multiply everything in the first bracket by everything in the second bracket - think of it as making sure everyone at two different tables meets everyone at the other table. This gives you x² - 3x - 10 after collecting like terms.
Top Tip: Always check your factorising by expanding the brackets back out - if you get your original expression, you've nailed it!
Squared brackets like ² are just the same bracket multiplied by itself twice. The difference of two squares pattern has a special shortcut: it always factors as x+4$$x-4.
2
of 2
Solving Quadratic Equations and Sequences
Quadratic equations are like puzzles where you're hunting for the mystery values of x that make everything equal zero. The standard form ax² + bx + c = 0 might look scary, but it follows a reliable three-step process: rearrange, factorise, then solve.
Once you've factorised your equation into something like x-4$$x-2 = 0, you're nearly there. Since anything multiplied by zero equals zero, either x-4 = 0 or x-2 = 0, giving you x = 4 or x = 2.
Sequences are number patterns that follow rules, and they're everywhere in maths. Linear sequences increase by the same amount each time (the common difference), while quadratic sequences have a constant second difference when you look at how the gaps between terms change.
Quick Check: For any quadratic sequence, find the first differences, then the second differences - if the second differences are constant, you've got a quadratic sequence!
Finding the nth term lets you calculate any term in the sequence without writing out hundreds of numbers. For linear sequences, use the format an + b, and for quadratic sequences, use an² + bn + c. The key is methodically working through the differences and checking your answer works.
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Maths1,138 views·Updated 7 Sept 2026·2 pagesMastering Quadratics: Knowledge Organizer for GCSE AQA
L
Luck@imbored2999
Ever wondered why algebra seems to follow patterns everywhere? Quadratics are like the building blocks of advanced maths - they're expressions where variables get squared (raised to the power of 2). Mastering how to expand, factorise, and solve these expressions...
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of 2
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Expanding and Factorising Quadratics
Think of expanding brackets like unpacking a suitcase - you're taking everything out and spreading it around. When you see something like 4, multiply the 4 by everything inside those brackets to get 4a + 24.
Factorising works the opposite way - you're packing things back into the suitcase by finding the Highest Common Factor (HCF). For example, 4x + 12 becomes 4 because 4 divides into both terms perfectly.
The real fun starts with double brackets like x-5$$x+2. You need to multiply everything in the first bracket by everything in the second bracket - think of it as making sure everyone at two different tables meets everyone at the other table. This gives you x² - 3x - 10 after collecting like terms.
Top Tip: Always check your factorising by expanding the brackets back out - if you get your original expression, you've nailed it!
Squared brackets like ² are just the same bracket multiplied by itself twice. The difference of two squares pattern has a special shortcut: it always factors as x+4$$x-4.
2
of 2Sign up to see the content. It's free!
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Solving Quadratic Equations and Sequences
Quadratic equations are like puzzles where you're hunting for the mystery values of x that make everything equal zero. The standard form ax² + bx + c = 0 might look scary, but it follows a reliable three-step process: rearrange, factorise, then solve.
Once you've factorised your equation into something like x-4$$x-2 = 0, you're nearly there. Since anything multiplied by zero equals zero, either x-4 = 0 or x-2 = 0, giving you x = 4 or x = 2.
Sequences are number patterns that follow rules, and they're everywhere in maths. Linear sequences increase by the same amount each time (the common difference), while quadratic sequences have a constant second difference when you look at how the gaps between terms change.
Quick Check: For any quadratic sequence, find the first differences, then the second differences - if the second differences are constant, you've got a quadratic sequence!
Finding the nth term lets you calculate any term in the sequence without writing out hundreds of numbers. For linear sequences, use the format an + b, and for quadratic sequences, use an² + bn + c. The key is methodically working through the differences and checking your answer works.
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Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
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Students love us, and so will you.
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