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What is (f−g)(x)(f - g)(x)?\newlinef(x)=−3x2f(x) = -3x^2\newlineg(x)=3x2+2xg(x) = 3x^2 + 2x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Full solution

Q. What is (f−g)(x)(f - g)(x)?\newlinef(x)=−3x2f(x) = -3x^2\newlineg(x)=3x2+2xg(x) = 3x^2 + 2x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______
  1. Write Expression: We have the functions f(x)=−3x2f(x) = -3x^2 and g(x)=3x2+2xg(x) = 3x^2 + 2x. Let's write down the expression for (f−g)(x)(f - g)(x).(f−g)(x)=f(x)−g(x)(f - g)(x) = f(x) - g(x)
  2. Substitute Functions: Now, let's substitute the given functions into the expression. \newline(f−g)(x)=(−3x2)−(3x2+2x)(f - g)(x) = (-3x^2) - (3x^2 + 2x)
  3. Distribute Negative Sign: Next, we distribute the negative sign through the parentheses to subtract g(x)g(x) from f(x)f(x).(f−g)(x)=−3x2−3x2−2x(f - g)(x) = -3x^2 - 3x^2 - 2x
  4. Combine Like Terms: Now, we combine like terms to simplify the expression. (f−g)(x)=−6x2−2x(f - g)(x) = -6x^2 - 2x

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