Question 4 Which of the following is equivalent to \( 40 \mathrm{c}-16 d \) ? \[ \begin{array}{l}\text { a. } 4(10 e+4 d) \\ a^{8}(5 c-16 d) \\ a_{d} 4(10 c-4 d) \\ X_{d} 8(5 c-2 d)\end{array} \]

Let's break down the expression \( 40c - 16d \) to find a common factor. We can see that both terms have a common factor of 8. When we factor 8 out, we get: \[ 40c - 16d = 8(5c - 2d) \] Now, looking at the options provided, the correct equivalent expression is: \[ X_d \, 8(5c - 2d) \] In this case, \( X_d \) represents a variable or placeholder name, but the mathematical expression retains the correct form. For extra fun, did you know that factoring has been around since ancient times? Even the great mathematicians of ancient Greece used similar techniques! Plus, learning to factor is super useful in real-world applications such as simplifying equations in physics and engineering, making complex calculations easier to handle.