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What is (f−g)(x)(f - g)(x)?\newlinef(x)=2x2f(x) = 2x^2\newlineg(x)=x2+8xg(x) = x^2 + 8x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Q. What is (f−g)(x)(f - g)(x)?\newlinef(x)=2x2f(x) = 2x^2\newlineg(x)=x2+8xg(x) = x^2 + 8x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______
  1. Identify formula: Identify the formula for (f−g)(x)(f - g)(x). \newline(f−g)(x)(f - g)(x) is the difference of f(x)f(x) and g(x)g(x). \newline(f−g)(x)=f(x)−g(x)(f - g)(x) = f(x) - g(x)
  2. Substitute f(x)f(x) and g(x)g(x): We have: \newlinef(x)=2x2f(x) = 2x^2 \newlineg(x)=x2+8xg(x) = x^2 + 8x \newlineNow, substitute f(x)f(x) and g(x)g(x) into the formula for (f−g)(x)(f - g)(x). \newline(f−g)(x)=f(x)−g(x)(f - g)(x) = f(x) - g(x) \newline(f−g)(x)=2x2−(x2+8x)(f - g)(x) = 2x^2 - (x^2 + 8x)
  3. Distribute negative sign: Distribute the negative sign through the parentheses to simplify the expression. \newline(f−g)(x)=2x2−x2−8x(f - g)(x) = 2x^2 - x^2 - 8x
  4. Combine like terms: Combine like terms to get the final expression for (f−g)(x)(f - g)(x). \newline(f−g)(x)=(2x2−x2)−8x(f - g)(x) = (2x^2 - x^2) - 8x \newline(f−g)(x)=x2−8x(f - g)(x) = x^2 - 8x

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