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3 Dec 2025
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Sofia Gibson
@sofiagibson_japn
This transcript covers various mathematical topics including multiplying and simplifying... Show more
This page delves into expanding and simplifying quadratic expressions, focusing on multiplying two binomials and squaring binomials.
Vocabulary: A quadratic expression is an algebraic expression of the second degree, typically in the form ax² + bx + c.
The page provides several examples of expanding binomial products:
Example: = x² + 7x + 3x + 21 = x² + 10x + 21
It also covers the special case of squaring binomials:
Example: ² = a² - 2ab + b²
Highlight: When expanding ², remember the formula a² + 2ab + b². This is different from ², which equals a² + b².
The page concludes with more complex examples involving algebraic terms:
Example: = x² - xm + yx - ym
This page focuses on expanding higher degree polynomials, including cubic expressions and more complex algebraic terms.
Vocabulary: A cubic expression is an algebraic expression of the third degree, typically in the form ax³ + bx² + cx + d.
The page provides several examples of expanding higher degree polynomials:
Example: = x³ + 5x² + 4x + 2x² + 10x + 8 = x³ + 7x² + 14x + 8
It also covers expanding the square of a binomial with a coefficient:
Example: ² = 4x² + 12x + 9
Highlight: When expanding ², remember the formula a²x² + 2abx + b². This is a generalization of the ² formula.
The page concludes with more complex examples involving negative terms and higher powers:
Example: = x³ - 7x² + 3x² - 21x - 2x² + 14x - 6x + 42 = x³ - 6x² - 13x + 42
This page focuses on solving problems involving distance, speed, and time using the formula D = S × T.
Definition: The formula D = S × T relates Distance (D), Speed (S), and Time (T). Distance is typically measured in kilometers or miles, speed in km/h or mph, and time in hours.
The page provides several examples of solving problems using this formula:
Example: If D = 50km and S = 20km/h, find T: T = D ÷ S = 50 ÷ 20 = 2.5 hours = 2 hours 30 minutes
Example: If D = 100 miles and T = 1 hour 25 minutes, find S: S = D ÷ T = 100 ÷ 1.416 ≈ 71 mph
Highlight: When solving these problems, it's crucial to ensure all units are consistent. Convert minutes to hours when necessary.
The page also introduces the concept of BEDO FORTS, which appears to be a mnemonic device for remembering formulas or steps in problem-solving, though its specific meaning is not explained in the given transcript.
This page compares and contrasts the Pythagorean theorem with trigonometric methods for solving trigonometry with right-angled triangles.
Definition: The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides: a² = b² + c².
Highlight: Both Pythagoras theorem and trigonometry involve right-angled triangles and finding lengths or angles within these triangles.
Key differences:
Example: Using Pythagoras theorem: a² = b² + c² Using trigonometry: sin θ = opposite / hypotenuse, cos θ = adjacent / hypotenuse, tan θ = opposite / adjacent
The page also briefly touches on factoring, including common factor factorization:
Example: 6y² - 12y = 6y
This page focuses on factoring trinomials, particularly quadratic expressions.
Definition: A trinomial is an algebraic expression consisting of three terms, often in the form ax² + bx + c.
The page provides several examples of factoring trinomials:
Example: x² + 7x + 10 =
Example: a² + 3a + 2 =
Highlight: When factoring trinomials, look for two numbers that multiply to give the constant term and add to give the coefficient of x.
The page also covers the special case of perfect square trinomials:
Example: x² + 2x + 1 = = ²
It concludes with a method for checking factorization by expanding the factors:
Example: For : 2 + 5 = 7 (coefficient of x) 2 × 5 = 10 (constant term)
This method provides a quick way to verify if the factorization is correct.
This page focuses on multiplying and simplifying algebraic expressions using the BODMAS rule. It covers single brackets, multiple brackets, and more complex expressions.
Definition: BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction. It defines the order of operations in mathematical expressions.
The page provides numerous examples of multiplying brackets and simplifying expressions, such as:
Example: 3 = 3x-6
Example: x = x² + 4x
It also demonstrates how to handle expressions with multiple terms and brackets:
Example: 3 - 5 = 3x+12 - 5x+15 = -2x+27
Highlight: When simplifying expressions with multiple terms, it's crucial to combine like terms and follow the BODMAS rule.
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
App Store
Google Play
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
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
Sofia Gibson
@sofiagibson_japn
This transcript covers various mathematical topics including multiplying and simplifying expressions, solving equations, factoring, and trigonometry. Here's a summary incorporating the guidelines:
A comprehensive guide to essential math concepts for students, covering multiplying and simplifying BODMAS steps, solving trigonometry... Show more
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This page delves into expanding and simplifying quadratic expressions, focusing on multiplying two binomials and squaring binomials.
Vocabulary: A quadratic expression is an algebraic expression of the second degree, typically in the form ax² + bx + c.
The page provides several examples of expanding binomial products:
Example: = x² + 7x + 3x + 21 = x² + 10x + 21
It also covers the special case of squaring binomials:
Example: ² = a² - 2ab + b²
Highlight: When expanding ², remember the formula a² + 2ab + b². This is different from ², which equals a² + b².
The page concludes with more complex examples involving algebraic terms:
Example: = x² - xm + yx - ym
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page focuses on expanding higher degree polynomials, including cubic expressions and more complex algebraic terms.
Vocabulary: A cubic expression is an algebraic expression of the third degree, typically in the form ax³ + bx² + cx + d.
The page provides several examples of expanding higher degree polynomials:
Example: = x³ + 5x² + 4x + 2x² + 10x + 8 = x³ + 7x² + 14x + 8
It also covers expanding the square of a binomial with a coefficient:
Example: ² = 4x² + 12x + 9
Highlight: When expanding ², remember the formula a²x² + 2abx + b². This is a generalization of the ² formula.
The page concludes with more complex examples involving negative terms and higher powers:
Example: = x³ - 7x² + 3x² - 21x - 2x² + 14x - 6x + 42 = x³ - 6x² - 13x + 42
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page focuses on solving problems involving distance, speed, and time using the formula D = S × T.
Definition: The formula D = S × T relates Distance (D), Speed (S), and Time (T). Distance is typically measured in kilometers or miles, speed in km/h or mph, and time in hours.
The page provides several examples of solving problems using this formula:
Example: If D = 50km and S = 20km/h, find T: T = D ÷ S = 50 ÷ 20 = 2.5 hours = 2 hours 30 minutes
Example: If D = 100 miles and T = 1 hour 25 minutes, find S: S = D ÷ T = 100 ÷ 1.416 ≈ 71 mph
Highlight: When solving these problems, it's crucial to ensure all units are consistent. Convert minutes to hours when necessary.
The page also introduces the concept of BEDO FORTS, which appears to be a mnemonic device for remembering formulas or steps in problem-solving, though its specific meaning is not explained in the given transcript.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page compares and contrasts the Pythagorean theorem with trigonometric methods for solving trigonometry with right-angled triangles.
Definition: The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides: a² = b² + c².
Highlight: Both Pythagoras theorem and trigonometry involve right-angled triangles and finding lengths or angles within these triangles.
Key differences:
Example: Using Pythagoras theorem: a² = b² + c² Using trigonometry: sin θ = opposite / hypotenuse, cos θ = adjacent / hypotenuse, tan θ = opposite / adjacent
The page also briefly touches on factoring, including common factor factorization:
Example: 6y² - 12y = 6y
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page focuses on factoring trinomials, particularly quadratic expressions.
Definition: A trinomial is an algebraic expression consisting of three terms, often in the form ax² + bx + c.
The page provides several examples of factoring trinomials:
Example: x² + 7x + 10 =
Example: a² + 3a + 2 =
Highlight: When factoring trinomials, look for two numbers that multiply to give the constant term and add to give the coefficient of x.
The page also covers the special case of perfect square trinomials:
Example: x² + 2x + 1 = = ²
It concludes with a method for checking factorization by expanding the factors:
Example: For : 2 + 5 = 7 (coefficient of x) 2 × 5 = 10 (constant term)
This method provides a quick way to verify if the factorization is correct.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page focuses on multiplying and simplifying algebraic expressions using the BODMAS rule. It covers single brackets, multiple brackets, and more complex expressions.
Definition: BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction. It defines the order of operations in mathematical expressions.
The page provides numerous examples of multiplying brackets and simplifying expressions, such as:
Example: 3 = 3x-6
Example: x = x² + 4x
It also demonstrates how to handle expressions with multiple terms and brackets:
Example: 3 - 5 = 3x+12 - 5x+15 = -2x+27
Highlight: When simplifying expressions with multiple terms, it's crucial to combine like terms and follow the BODMAS rule.
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Google Play
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
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
