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Simplifying (fg)(x) = (x2 + -9)(5x + 20) Multiply fg * x fgx = (x2 + -9)(5x + 20) Reorder the terms: fgx = (-9 + x2)(5x + 20) Reorder the terms: fgx = (-9 + x2)(20 + 5x) Multiply (-9 + x2) * (20 + 5x) fgx = (-9(20 + 5x) + x2(20 + 5x)) fgx = ((20 * -9 + 5x * -9) + x2(20 + 5x)) fgx = ((-180 + -45x) + x2(20 + 5x)) fgx = (-180 + -45x + (20 * x2 + 5x * x2)) fgx = (-180 + -45x + (20x2 + 5x3)) fgx = (-180 + -45x + 20x2 + 5x3) Solving fgx = -180 + -45x + 20x2 + 5x3 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'gx'. f = -180g-1x-1 + -45g-1 + 20g-1x + 5g-1x2 Simplifying f = -180g-1x-1 + -45g-1 + 20g-1x + 5g-1x2 Reorder the terms: f = -45g-1 + -180g-1x-1 + 20g-1x + 5g-1x2
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