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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=2x2f(x) = 2x^2\newlineg(x)=−2x+2g(x) = -2x + 2\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)=−2x+2g(x) = -2x + 2\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).(f∗g)(x)(f * g)(x) is the product of f(x)f(x) and g(x)g(x).(f∗g)(x)=f(x)∗g(x)(f * g)(x) = f(x) * g(x)
  2. Multiply Functions: We have:\newlinef(x)=2x2f(x) = 2x^2\newlineg(x)=−2x+2g(x) = -2x + 2\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(2x2)∗(−2x+2)(f * g)(x) = (2x^2) * (-2x + 2)
  3. Distribute Terms: Distribute 2x22x^2 to both terms in g(x)g(x). \newline(f⋅g)(x)=2x2⋅(−2x)+2x2⋅2(f \cdot g)(x) = 2x^2 \cdot (-2x) + 2x^2 \cdot 2
  4. Perform Multiplication: Perform the multiplication.\newline(f⋅g)(x)=−4x3+4x2(f \cdot g)(x) = -4x^3 + 4x^2
  5. Simplify Polynomial: Express your answer as a simplified polynomial.\newlineThe polynomial −4x3+4x2-4x^3 + 4x^2 is already in its simplest form.

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