To simplify the expression \((2x + 1)(x - 4)\), we will use the distributive property (also known as the FOIL method for binomials).
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First, multiply the first terms: \(2x \cdot x = 2x^2\)
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Next, multiply the outer terms: \(2x \cdot (-4) = -8x\)
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Then, multiply the inner terms: \(1 \cdot x = x\)
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Finally, multiply the last terms: \(1 \cdot (-4) = -4\)
Now, combine all these results: \[ 2x^2 - 8x + x - 4 \]
Combine the like terms \(-8x\) and \(x\): \[ 2x^2 - 7x - 4 \]
Thus, the simplified expression is: \[ 2x^2 - 7x - 4 \]
The correct answer is D: 2x^2 - 7x - 4.
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