Question Multiply and collect like terms: \( (8 p+4 q)(p-3 q) \)

To multiply \( (8p + 4q)(p - 3q) \), you'll want to apply the distributive property, also known as the FOIL method for two binomials. First, multiply each term in the first binomial by each term in the second binomial: 1. \( 8p \cdot p = 8p^2 \) 2. \( 8p \cdot (-3q) = -24pq \) 3. \( 4q \cdot p = 4pq \) 4. \( 4q \cdot (-3q) = -12q^2 \) Now, combine these results: \[ 8p^2 + (-24pq) + (4pq) + (-12q^2) \] Next, combine like terms, specifically the \(pq\) terms: \[ 8p^2 - 24pq + 4pq - 12q^2 = 8p^2 - 20pq - 12q^2 \] So, the final simplified result is: \[ 8p^2 - 20pq - 12q^2 \]