To simplify the expression \((2x + 4)(7x - 1)\), we can use the distributive property (also known as the FOIL method for binomials):
\[ (2x + 4)(7x - 1) = 2x(7x) + 2x(-1) + 4(7x) + 4(-1) \]
Calculating each term:
- \(2x \cdot 7x = 14x^2\)
- \(2x \cdot (-1) = -2x\)
- \(4 \cdot 7x = 28x\)
- \(4 \cdot (-1) = -4\)
Now, combine all these terms together:
\[ 14x^2 - 2x + 28x - 4 \]
Combine the like terms \(-2x\) and \(28x\):
\[ 14x^2 + (28x - 2x) - 4 = 14x^2 + 26x - 4 \]
Thus, the simplified expression is:
\[ 14x^2 + 26x - 4 \]
Since there's no option that matches \(14x^2 + 26x - 4\) in your provided responses, please double-check to see if there was a mistake in the options given. The correct calculation yields \(14x^2 + 26x - 4\).