Example Question - expand binomial

Simplifying Expressions Using the Distributive Property

1. Apply the distributive property to 3p(p - q): 3p * p - 3p * q = 3p^2 - 3pq 2. Expand the square of the binomial (2p - q)^2: (2p - q)(2p - q) = 4p^2 - 4pq + q^2 3. Subtract the expanded binomial from the first expression: (3p^2 - 3pq) - (4p^2 - 4pq + q^2) 4. Distribute the negative sign to each term in the second expression: 3p^2 - 3pq - 4p^2 + 4pq - q^2 5. Combine like terms: -p^2 + pq - q^2 So the simplified expression is: -p^2 + pq - q^2