\#1/16 Multiplying Polynomials \( \begin{array}{l}(n-5)(3 n-4) \\ 3 n^{2}-19 n+20 \\ 3 n^{2}-19 n-20 \\ 3 n^{2}+19 n-20 \\ 3 n^{2}-11 n+20\end{array} \)

When multiplying polynomials, like \( (n-5)(3n-4) \), you can use the distributive property, commonly known as the FOIL method (First, Outside, Inside, Last) for binomials. Here’s a breakdown: First: \(n \cdot 3n = 3n^2\), Outside: \(n \cdot -4 = -4n\), Inside: \(-5 \cdot 3n = -15n\), and Last: \(-5 \cdot -4 = 20\). Combine like terms, and you get \(3n^2 - 19n + 20\) as your final answer. In real-world applications, multiplying polynomials can be visualized in areas such as physics, engineering, and economics where relationships between variables need to be captured. For example, the area of a rectangular plot of land can be expressed as a polynomial, which you would multiply out when calculating total area based on length and width given in polynomial terms. So, that quick math with polynomials can save a lot of headaches down the road!