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Simplifying f(n) = n(8n2 + 4n)(2n + 2) Multiply f * n fn = n(8n2 + 4n)(2n + 2) Reorder the terms: fn = n(4n + 8n2)(2n + 2) Reorder the terms: fn = n(4n + 8n2)(2 + 2n) Multiply (4n + 8n2) * (2 + 2n) fn = n(4n * (2 + 2n) + 8n2 * (2 + 2n)) fn = n((2 * 4n + 2n * 4n) + 8n2 * (2 + 2n)) fn = n((8n + 8n2) + 8n2 * (2 + 2n)) fn = n(8n + 8n2 + (2 * 8n2 + 2n * 8n2)) fn = n(8n + 8n2 + (16n2 + 16n3)) Combine like terms: 8n2 + 16n2 = 24n2 fn = n(8n + 24n2 + 16n3) fn = (8n * n + 24n2 * n + 16n3 * n) fn = (8n2 + 24n3 + 16n4) Solving fn = 8n2 + 24n3 + 16n4 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'n'. f = 8n + 24n2 + 16n3 Simplifying f = 8n + 24n2 + 16n3
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