\begin{tabular}{l} Multiply the following and collect like terms: \\ \( \qquad(2 x-5)(3 x-1) \) \\ Select the correct answer below: \\ \( 6 x^{2}-13 x+5 \) \\ \( 6 x^{2}-17 x-5 \) \\ \( 6 x^{2}-13 x-5 \) \\ \( 6 x^{2}-17 x+5 \) \\ \( 6 x^{2}+13 x-5 \) \\ \hline\end{tabular}
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To multiply \( (2x-5)(3x-1) \), we'll use the distributive property (often called the FOIL method for binomials). First, multiply the first terms: \( 2x \cdot 3x = 6x^2 \). Next, multiply the outer terms: \( 2x \cdot -1 = -2x \). Then, the inner terms: \( -5 \cdot 3x = -15x \). Finally, multiply the last terms: \( -5 \cdot -1 = 5 \). Now, combine all these results: \( 6x^2 - 2x - 15x + 5 \). Combine the like terms: \( 6x^2 - 17x + 5 \). Hence, the correct answer is: \( 6x^{2}-17x+5 \). Here's the summary of your solution: **Multiply, combine like terms, and you'll arrive at the solution!**
