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Fun with Quadratics: Factorizing, Expanding Brackets, and Substitution

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Raid_BK

28/12/2022

Maths

Topic 1- Algebra Basics

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Algebraic expressions

Fun with Quadratics: Factorizing, Expanding Brackets, and Substitution

A comprehensive guide to basic algebraic operations focusing on factorisation of quadratic expressions and expanding quadratic expressions with brackets.

  • Covers essential algebraic concepts including variables, expressions, equations, and formulae
  • Explains quadratic expansion techniques with detailed step-by-step examples
  • Demonstrates factorisation methods for various types of quadratic expressions
  • Includes important rules for substitution method in basic algebra
  • Provides clear examples of working with positive and negative numbers in brackets
...

28/12/2022

655

- Quadratic expanstion +5t 1,5m² +3m + 8 Quadratic expantion where the highest power of 182 For example, y², 3t² expression Multing everythi

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Page 2: Basic Algebra and Substitution

This page covers fundamental algebraic concepts and the substitution method, along with practical examples of factorisation.

Definition: Variables are letters used to represent numbers, while expressions are combinations of letters and numbers.

Vocabulary: An equation contains an equals sign and at least one variable, while a formula involves multiple variables.

Highlight: When performing substitution, always use brackets around negative numbers to avoid calculation errors.

Example: To find the value of 3x² - 5 when x = 3:

  1. Write 333² - 5
  2. Calculate the result using proper order of operations

The page emphasizes the importance of identifying common factors in factorisation:

  • Look for common coefficients first
  • Then identify common variables
  • Express the factored form using brackets

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Subjects

Maths

Algebra

Algebraic expressions

 

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655

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28 Dec 2022

•

2 pages

Fun with Quadratics: Factorizing, Expanding Brackets, and Substitution

user profile picture

Raid_BK

@noraid_bk

A comprehensive guide to basic algebraic operations focusing on factorisation of quadratic expressions and expanding quadratic expressions with brackets.

  • Covers essential algebraic concepts including variables, expressions, equations, and formulae
  • Explains quadratic expansion techniques with detailed step-by-step examples
  • Demonstrates factorisation... Show more

- Quadratic expanstion +5t 1,5m² +3m + 8 Quadratic expantion where the highest power of 182 For example, y², 3t² expression Multing everythi

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Page 2: Basic Algebra and Substitution

This page covers fundamental algebraic concepts and the substitution method, along with practical examples of factorisation.

Definition: Variables are letters used to represent numbers, while expressions are combinations of letters and numbers.

Vocabulary: An equation contains an equals sign and at least one variable, while a formula involves multiple variables.

Highlight: When performing substitution, always use brackets around negative numbers to avoid calculation errors.

Example: To find the value of 3x² - 5 when x = 3:

  1. Write 333² - 5
  2. Calculate the result using proper order of operations

The page emphasizes the importance of identifying common factors in factorisation:

  • Look for common coefficients first
  • Then identify common variables
  • Express the factored form using brackets
- Quadratic expanstion +5t 1,5m² +3m + 8 Quadratic expantion where the highest power of 182 For example, y², 3t² expression Multing everythi

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Quadratic Expressions and Factorisation

This page introduces the fundamental concepts of quadratic expressions and their manipulation through expansion and factorisation. The content focuses on methods for expanding bracket expressions and factorising quadratic terms.

Definition: Quadratic expressions are algebraic expressions where the highest power of a variable is 2, such as y² or 3t².

Example: When expanding x+3x + 3x+4x + 4, multiply each term in the first bracket by each term in the second bracket.

Highlight: For factorisation of expressions like x² + ax + b, the expression inside each bracket will start with x, and the signs in the brackets depend on the original expression's signs.

Vocabulary: Factorisation is the process of converting a quadratic expression back into its bracket form.

The page outlines different patterns for factorising quadratic expressions:

  • x² + ax + b = x+?x + ?x+?x + ?
  • x² + ax - b = x+?x + ?x−?x - ?
  • x² - ax + b = x−?x - ?x−?x - ?

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Paul T

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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

Android user

This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

Android user

I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

iOS user