b. \( (2 M-5)(4 M+1) \)

Let's dive into the world of polynomial multiplication! When you multiply \( (2 M - 5)(4 M + 1) \), you can apply the distributive property—also known as the FOIL method for binomials. This means you multiply each term in the first binomial by each term in the second. So, you get \( 2M \cdot 4M + 2M \cdot 1 - 5 \cdot 4M - 5 \cdot 1 \), which simplifies to \( 8M^2 + 2M - 20M - 5 \). Collecting like terms yields \( 8M^2 - 18M - 5 \). Voilà! Now, for some problem-solving tips: Be careful with signs! It’s all too easy to drop a negative or mix up addition and subtraction when you're juggling multiple terms. A great way to catch mistakes is to double-check each step or even use a different color for each binomial during multiplication. Happy multiplying!