Concept:To expand the product (7r−5)(3r+4), we multiply each term inside the first bracket by the whole second bracket, then simplify.Explanation:Use the distributive law: (a−b)(c+d)=a(c+d)−b(c+d).Applying it, (7r−5)(3r+4)=7r(3r+4)−5(3r+4).Now multiply each part: 7r(3r+4)=7r×3r+7r×4=21r2+28r.And −5(3r+4)=−5×3r−5×4=−15r−20.Combining the results: 21r2+28r−15r−20.Simplify like terms 28r−15r=13r.So the expanded expression becomes 21r2+13r−20.This matches option A.Answer:21r2+13r−20, which is option A.