Expand and simplify \( (7-v)(5 v+3) \)

To expand the expression \( (7-v)(5v+3) \), we can use the distributive property (also known as the FOIL method for binomials). First, distribute \( 7 \) to both terms in the second binomial: \[ 7 \cdot 5v + 7 \cdot 3 = 35v + 21 \] Next, distribute \( -v \) to both terms in the second binomial: \[ -v \cdot 5v - v \cdot 3 = -5v^2 - 3v \] Now, combine all the terms we expanded: \[ 35v + 21 - 5v^2 - 3v \] Combine like terms: \[ -5v^2 + (35v - 3v) + 21 = -5v^2 + 32v + 21 \] So, the expanded and simplified expression is: \[ \boxed{-5v^2 + 32v + 21} \]