Find the product. Simplify your answer. \[ (4 d-3)(4 d-4) \]

To find the product of the two binomials \((4d - 3)(4d - 4)\), you can use the **FOIL** method, which stands for **First**, **Outer**, **Inner**, and **Last** terms multiplication. Here's a step-by-step breakdown: 1. **First:** Multiply the first terms in each binomial. \[ 4d \times 4d = 16d^2 \] 2. **Outer:** Multiply the outer terms in the product. \[ 4d \times (-4) = -16d \] 3. **Inner:** Multiply the inner terms. \[ (-3) \times 4d = -12d \] 4. **Last:** Multiply the last terms in each binomial. \[ (-3) \times (-4) = 12 \] Now, combine all these results: \[ 16d^2 - 16d - 12d + 12 \] Next, combine like terms (the terms with \(d\)): \[ -16d - 12d = -28d \] So, the simplified product is: \[ 16d^2 - 28d + 12 \] **Final Answer:** \[ 16d^2 - 28d + 12 \]