# Number grids. In this investigation I have been attempting to work out a formula that will find the difference between the products of the top left and bottom right of a number grid and the top right and bottom left of a number grid.

In this investigation I have been attempting to work out a formula that will find the difference between the products of the top left and bottom right of a number grid and the top right and bottom left of a number grid.

A 10x10 number grid

If you choose any 2x2 box on a 10x10 number grid then the difference should equal 10…

35x46=1610

Difference=10

36x45=1620

The difference equals 10. So what would happen if you tried the same thing with a 3x3 box?

37x19=703

Difference=40

17x39=663

The difference equals 40. So if you try it with a 4x4 box…

61x94=5734

Difference=90

91x64=5824

The difference equals 90. Lets just try one more:

55x99=5445

Difference=160

95x59=5605

We now have enough results.

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#### Here's what a teacher thought of this essay

A well written piece of work with only a couple of minor errors. This piece of work shows an excellent application of multiplying double brackets. 4 stars ****