\#1/16 Multiplying Polynomials \( \begin{array}{l}(2 x-6)(x+3) \\ 2 x^{2}+12 x-18 \\ 2 x^{2}-12 x-18 \\ 2 x^{2}+18 \\ 2 x^{2}-18\end{array} \)

To find the product of the polynomials \( (2x - 6)(x + 3) \), we can use the distributive property (also known as the FOIL method for binomials). When multiplying, we distribute each term in the first polynomial to each term in the second: \[ 2x \cdot x + 2x \cdot 3 - 6 \cdot x - 6 \cdot 3 = 2x^2 + 6x - 6x - 18 \] After combining like terms (the \(6x\) and \(-6x\) cancel each other), we are left with: \[ 2x^2 - 18 \] So, the answer is \(2x^2 - 18\). Keep in mind that when multiplying polynomials, always watch for like terms that can be combined for a simpler expression. If you miss any, you might end up with a more complicated answer than necessary! Always double-check your work, especially when dealing with signs like the negative in \(-6\). They can sneak in and cause confusion if you're not careful!