1. Apply the distributive property: (3q - 1)(10q + 7) = 3q(10q) + 3q(7) - 1(10q) - 1(7)
2. Calculate each term: 3q \cdot 10q = 30q^2, 3q \cdot 7 = 21q, -1 \cdot 10q = -10q, -1 \cdot 7 = -7
3. Combine like terms: 30q^2 + 21q - 10q - 7 = 30q^2 + 11q - 7
Answer: 30q^2 + 11q - 7