644 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!

1 year ago

Answered by Alexander, a GCSE Maths tutor with MyTutor

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

#### 780 SUBJECT SPECIALISTS

£18 /hr

Degree: Mathematics (Masters) - Bath University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“Hi! I am studying Mathematics at Bath University and I am passionate about teaching, and learning mathematics.”

MyTutor guarantee

|  1 completed tutorial

£18 /hr

Degree: General Engineering (Masters) - Durham University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Second year Engineering student, I'm passionate, dedicated and personable. A- Level Maths and Physics (A*AA).”

MyTutor guarantee

£18 /hr

Degree: Medicinal and biological chemistry (Integrated Masters) - Nottingham University

Subjects offered:Maths, Chemistry+ 1 more

Maths
Chemistry
Biology

“Hi! I'm a Chemistry student studying at the University of Nottingham with a passion for science that I'd love to pass on to my tutees!”

MyTutor guarantee

Currently unavailable: for regular students

Degree: Accountancy (Bachelors) - Durham University

Subjects offered:Maths, French+ 5 more

Maths
French
English Literature
English Language
Dutch
-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 complete the square of an equation?