Answer:
To simplify the expression (x - 4)(x^2 - 3x - 9), we need to apply the distributive property. This means that we need to multiply each term in the first parentheses by each term in the second parentheses. Let's break it down step-by-step:
First, distribute x from the first parentheses to each term in the second parentheses:
x * x^2 = x^3
x * (-3x) = -3x^2
x * (-9) = -9x
Next, distribute -4 from the first parentheses to each term in the second parentheses:
-4 * x^2 = -4x^2
-4 * (-3x) = 12x
-4 * (-9) = 36
Now, let's combine like terms:
x^3 + (-3x^2) + (-9x) + (-4x^2) + 12x + 36
Combine the x^2 terms: -3x^2 + (-4x^2) = -7x^2
Combine the x terms: -9x + 12x = 3x
The simplified expression is: x^3 - 7x^2 + 3x + 36
Therefore, the correct answer is b) x^3 - 7x^2 + 3x + 36.
Explanation:
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