MYTUTOR SUBJECT ANSWERS

236 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, ...

5 months ago

Answered by Alexander, a GCSE Maths tutor with MyTutor


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

329 SUBJECT SPECIALISTS

£22 /hr

George S.

Degree: Combined Honours (English Literature and Spanish) (Bachelors) - Durham University

Subjects offered: Maths, Spanish+ 3 more

Maths
Spanish
German
English
-Personal Statements-

“Hi, I'm George - a Spanish and English undergraduate. I would love to tutor anybody studying English or Spanish (and GCSE or A Level), as well as GCSE German and Maths!”

£18 /hr

Angeliki H.

Degree: Economics (Bachelors) - Bristol University

Subjects offered: Maths, Economics

Maths
Economics

“Hi, I am Angeliki! I am an economics student at the University of Bristol. Economics have always been my passion. Through my tutorials I will be able to pass my love and excitement about the subject to my students making it more inter...”

MyTutor guarantee

£18 /hr

James S.

Degree: Russian Studies and Politics, Economics (Bachelors) - Edinburgh University

Subjects offered: Maths

Maths

“Hi, I'm James and I'm studying Russian, Politics and Economics at the University of Edinburgh! Having spent a year as a Gap Tutor at Harrow International School Hong Kong and helping students to develop their understanding of mathemat...”

MyTutor guarantee

About the author

Alexander C.

Currently unavailable: for regular students

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 I find the equation of a straight line?

Solve the following to find x. x^2 +3x -10 =0

How do I solve x^2+6x+8=0?

Solve the simultaneous equations: y = 4x^2 - 9x - 1 and y = 5 - 4x

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