What is the easiest way to expand quadratic equations?

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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, ...

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