Find the product: \( (8 n-3)(5 n+7) \) \( 40 n^{2}-21 \) \( 13 n^{2}+17 n+4 \) \( 40 n^{2}-41 n-21 \) \( 40 n^{2}+41 n-21 \)

To find the product of the binomials \( (8n - 3)(5n + 7) \), we can use the distributive property (also known as the FOIL method for binomials): \[ (8n - 3)(5n + 7) = 8n \cdot 5n + 8n \cdot 7 - 3 \cdot 5n - 3 \cdot 7 \] Let's calculate each term step by step: 1. **First Terms:** \( 8n \cdot 5n = 40n^2 \) 2. **Outer Terms:** \( 8n \cdot 7 = 56n \) 3. **Inner Terms:** \( -3 \cdot 5n = -15n \) 4. **Last Terms:** \( -3 \cdot 7 = -21 \) Now, combine all the terms: \[ 40n^2 + 56n - 15n - 21 \] Combine like terms: \[ 40n^2 + (56n - 15n) - 21 = 40n^2 + 41n - 21 \] **Final Answer:** \[ 40n^{2} + 41n - 21 \] This corresponds to the fourth option: \[ 40 n^{2}+41 n-21 \]