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Simplifying (fg)(x) = (2x2 + -25x + 72)(x + -8) Multiply fg * x fgx = (2x2 + -25x + 72)(x + -8) Reorder the terms: fgx = (72 + -25x + 2x2)(x + -8) Reorder the terms: fgx = (72 + -25x + 2x2)(-8 + x) Multiply (72 + -25x + 2x2) * (-8 + x) fgx = (72(-8 + x) + -25x * (-8 + x) + 2x2 * (-8 + x)) fgx = ((-8 * 72 + x * 72) + -25x * (-8 + x) + 2x2 * (-8 + x)) fgx = ((-576 + 72x) + -25x * (-8 + x) + 2x2 * (-8 + x)) fgx = (-576 + 72x + (-8 * -25x + x * -25x) + 2x2 * (-8 + x)) fgx = (-576 + 72x + (200x + -25x2) + 2x2 * (-8 + x)) fgx = (-576 + 72x + 200x + -25x2 + (-8 * 2x2 + x * 2x2)) fgx = (-576 + 72x + 200x + -25x2 + (-16x2 + 2x3)) Combine like terms: 72x + 200x = 272x fgx = (-576 + 272x + -25x2 + -16x2 + 2x3) Combine like terms: -25x2 + -16x2 = -41x2 fgx = (-576 + 272x + -41x2 + 2x3) Solving fgx = -576 + 272x + -41x2 + 2x3 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'gx'. f = -576g-1x-1 + 272g-1 + -41g-1x + 2g-1x2 Simplifying f = -576g-1x-1 + 272g-1 + -41g-1x + 2g-1x2 Reorder the terms: f = 272g-1 + -576g-1x-1 + -41g-1x + 2g-1x2
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