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Algebraic Investigation 1: Square Boxes on a 10x10 Grid In this first investigation, the difference in products of the alternate corners of a square, equal-sided box on a 10x10 gridsquare will be investigated. It is believed that the products and their differences should demonstrate a constant pattern no matter what dimensions are used; as long as they remain equal. In order to prove this, both a numeric and algebraic method will be used in order to calculate this difference. The numeric method will help establish a baseline set of numbers for testing, and to help in the establishment of a set of algebraic formulae for use on an n x n gridsquare. In the example gridsquare below, the following method is used in order to calculate the difference between the products of opposite corners. (a) (b) (c) (d) Stage A: Top left number x Bottom right number = (a) multiplied by (d) Stage B: Bottom left number x Top right...

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