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You may know that (x + y)(x - y) = x^2 - y^2. You can use this to find short-cuts to multiplying! To find the product of two numbers, we will transform both numbers -- one into a sum, the other into a difference. Start by finding their average (the mean, or simply, the number half-way between them). Now, find the difference for each number to this average. Your larger number can be changed into the sum of the average and the difference, and the smaller number is the difference of the average and the difference. For example: 18 * 12 The average is 15, and each is 3 away from that number: 18 = 15 +3, and 12 = 15 - 3. We can now re-write: 18 * 12 = (15 + 3)(15 - 3). This is now in the precise format of the equation above. Thus: 18 * 12 = (15 + 3)(15 - 3) = 15^2 - 3^2 = 225 - 9 = 216 Example I: 12 * 8 = (10 + 2)(10 - 2) = 10^2 - 2^2 = 100 - 4 = 96 Example II: 33 * 17 = (25 + 8)(25 - 8) = 625 - 64 = 561 Example III: 314 * 286 =... read more

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