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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−4x+4f(x) = -4x + 4\newlineg(x)=−4xg(x) = -4x\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)=−4x+4f(x) = -4x + 4\newlineg(x)=−4xg(x) = -4x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______
  1. Multiply Functions: To find the product of two functions, we multiply them together. We have f(x)=−4x+4f(x) = -4x + 4 and g(x)=−4xg(x) = -4x. The product (f∗g)(x)(f * g)(x) is found by multiplying f(x)f(x) by g(x)g(x).\newlineCalculation: (f∗g)(x)=f(x)∗g(x)=(−4x+4)∗(−4x)(f * g)(x) = f(x) * g(x) = (-4x + 4) * (-4x)
  2. Distribute Multiplication: Now we distribute the multiplication across the terms in the parentheses.\newlineCalculation: (−4x+4)×(−4x)=(−4x×−4x)+(4×−4x)(-4x + 4) \times (-4x) = (-4x \times -4x) + (4 \times -4x)
  3. Simplify Terms: Next, we simplify each term.\newlineCalculation: (−4x×−4x)=16x2(-4x \times -4x) = 16x^2 and (4×−4x)=−16x(4 \times -4x) = -16x
  4. Combine Final Polynomial: Combine the simplified terms to get the final polynomial.\newlineCalculation: 16x2−16x16x^2 - 16x

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