MYTUTOR SUBJECT ANSWERS

157 views

What is the easiest way to expand quadratic equations?

There are many methods of expanding quadratic equations, however there is one method which I find to be far easier than the others. This method is called the "box method", and allows this to be done quickly and reliably!

Here is an example. Take this example question : Expand the quadratic equation ( x + 2 ) * ( x + 3 ). 

First, you must draw a box divided into 4 quarters, as shown: 

__________________

|________|_________|

|________|_________|

Then, you need to place one of the brackets on the top and on the left side of this box, as below: 

   ____x________3____

x |____a___|_____b___|

2 |____c___|_____d___|

Then all you need to do is muliply the number or variable on the top of the box, and on the side of the box. 

Box A therefore is : x * x = x2

Box B therefore is 3 * x = 3x

Box C therefore is 2 * x = 2x

Box C therefore is 3 * 2 = 6

Then just add up all of the results and simplify : x2 + 3x + 2x + 6 = x+ 5x + 6

This method also works if you have more than two figures in each bracket, so if you get asked to expand the following, you simply follow the steps again!

Expand (x+ 4x+ 5x + 7) * (x + 2) 

First, you must draw a rectangle of two boxes in height, but simply make it longer!

   ____x3_______4x2_______5x___________ _7___

x |____a____|______b___|______c___|_____d____|

|____e____|_____f ____|______g___|_____h____|

Then follow the same steps again, multiplying one side of the box by the other

Box A : x3 * x = x4

Box B : 4x2 * x = 4x3

Box C : x * 5x = 5x2

Box D : 7 * x = 7x

Box E : 2 * x3 = 2x3

Box F : 4x2 * 2 = 8x2

Box G : 2 * 5x = 10x

Box H : 2 * 7 = 14

Add them all up to get : x4 + 4x3 + 2x+ 5x+ 8x+ 7x +10x +14 = x+ 6x3 + 13x2 + 17x +14. 

And there you go! The easiest and quickest way to expand a quadratic equation!

Alexander C. IB Business Studies tutor, GCSE Business Studies tutor, ...

4 months ago

Answered by Alexander, a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

327 SUBJECT SPECIALISTS

£18 /hr

Rhoda A.

Degree: Electrical and Electronic Engineering (Masters) - Sheffield University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“A Bit About MeI have just finished my second year at The University of Sheffield, studying Electrical and Electronic Engineering.I have always wanted to teach maths, this was because I had a great teacher (my dad). I believe that e...”

£18 /hr

Seb G.

Degree: Mathematics (Masters) - Bath University

Subjects offered: Maths

Maths

“Me: I'm a second year maths student at the University of Bath. I fell in love with maths after a rocky start with the subject, so believe that I can help people regardless of whether they like maths or not.  I've been tutoring maths l...”

MyTutor guarantee

£24 /hr

Robbie H.

Degree: Engineering Design (Masters) - Bristol University

Subjects offered: Maths, Physics

Maths
Physics

“I am a 22 year old Master's student at the University of Bristol studying Engineering Design. I achieved a First in my Bachelors and A*A*A at A Level. I have apassion for maths and science and hope that in my sessions some of this wil...”

MyTutor guarantee

About the author

£18 /hr

Alexander C.

Degree: Accountancy (Bachelors) - Durham University

Subjects offered: Maths, French+ 5 more

Maths
French
English Literature
English Language
Dutch
Business Studies
-Personal Statements-

“Hi! My name is Alex, and I am currently a student at Durham University, studying Accountancy! I came to Durham from The Netherlands, having spent my entire life there, but have British and French parents. Having gone to an internation...”

You may also like...

Other GCSE Maths questions

How do you use the pythagoras equation?

How to solve an equation when the variable is in the denominator?

GCSE Maths - Solve the equation (2x+3)/(x-4) - (2x-8)/(2x+1) = 1 Give your answer to 2 decimal places.

If f(x)=8x-3, what is the inverse function?

View GCSE Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok