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Simplifying S = n(n + 1)(2n + 1) Reorder the terms: S = n(1 + n)(2n + 1) Reorder the terms: S = n(1 + n)(1 + 2n) Multiply (1 + n) * (1 + 2n) S = n(1(1 + 2n) + n(1 + 2n)) S = n((1 * 1 + 2n * 1) + n(1 + 2n)) S = n((1 + 2n) + n(1 + 2n)) S = n(1 + 2n + (1 * n + 2n * n)) S = n(1 + 2n + (1n + 2n2)) Combine like terms: 2n + 1n = 3n S = n(1 + 3n + 2n2) S = (1 * n + 3n * n + 2n2 * n) S = (1n + 3n2 + 2n3) Solving S = 1n + 3n2 + 2n3 Solving for variable 'S'. Move all terms containing S to the left, all other terms to the right. Simplifying S = 1n + 3n2 + 2n3
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