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1 million = 1,000,000 = 1000² Which means we want: (1000 + 1)² - (1000 - 1)² , that is 1001² - 999² However, before we work that out, lets look at what we have. let a = 1000, b = 1, then: (1000 + 1)² - (1000 - 1)² = (a + b)² - (a - b)² Now (a + b)² = a² +2ab + b² and (a - b)² = a² - 2ab - b² → (a + b)² - (a - b)² = a² +2ab + b² - (a² - 2ab - b²) = 4ab As a = 1000, b = 1, this means (1000 + 1)² - (1000 -1)² = 4 × 1000 × 1 = 4000.
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Let x = abc be a 3-digit number. The expanded for of x is 100*a + 10*b + c.And let y = de = 10*d + e be a 2-digit number. Then x*y = 1000*a*d + 100*a*e + 100*b*d + 10*b*e + 10*c*d + c*e = 1000*a*d + 100*(a*e + b*d) + 10*(b*e + c*d) + c*e.