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Simplifying g(r) = (5r3 + 3r + 1)(r2 + 3) Multiply g * r gr = (5r3 + 3r + 1)(r2 + 3) Reorder the terms: gr = (1 + 3r + 5r3)(r2 + 3) Reorder the terms: gr = (1 + 3r + 5r3)(3 + r2) Multiply (1 + 3r + 5r3) * (3 + r2) gr = (1(3 + r2) + 3r * (3 + r2) + 5r3 * (3 + r2)) gr = ((3 * 1 + r2 * 1) + 3r * (3 + r2) + 5r3 * (3 + r2)) gr = ((3 + 1r2) + 3r * (3 + r2) + 5r3 * (3 + r2)) gr = (3 + 1r2 + (3 * 3r + r2 * 3r) + 5r3 * (3 + r2)) gr = (3 + 1r2 + (9r + 3r3) + 5r3 * (3 + r2)) gr = (3 + 1r2 + 9r + 3r3 + (3 * 5r3 + r2 * 5r3)) gr = (3 + 1r2 + 9r + 3r3 + (15r3 + 5r5)) Reorder the terms: gr = (3 + 9r + 1r2 + 3r3 + 15r3 + 5r5) Combine like terms: 3r3 + 15r3 = 18r3 gr = (3 + 9r + 1r2 + 18r3 + 5r5) Solving gr = 3 + 9r + 1r2 + 18r3 + 5r5 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Divide each side by 'r'. g = 3r-1 + 9 + r + 18r2 + 5r4 Simplifying g = 3r-1 + 9 + r + 18r2 + 5r4 Reorder the terms: g = 9 + 3r-1 + r + 18r2 + 5r4
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