Example Question - distribution method

Solving the Expression with Distribution and Expansion

To solve the expression given in the image: 1. Distribute the \( 3p \) across \( (p - q) \): \[ 3p \cdot p + 3p \cdot (-q) \] 2. Expand the square \( (2p - q)^2 \) using the FOIL (First, Outer, Inner, Last) method: \[ (2p - q)(2p - q) \] \[ 2p \cdot 2p + 2p \cdot (-q) + (-q) \cdot 2p + (-q) \cdot (-q) \] Combine the above expansions: \[ 3p^2 - 3pq - (4p^2 - 2pq - 2pq + q^2) \] 3. Expand the negative sign into the second parenthesis: \[ 3p^2 - 3pq - 4p^2 + 2pq + 2pq - q^2 \] 4. Combine like terms: \[ 3p^2 - 4p^2 - 3pq + 2pq + 2pq - q^2 \] \[ -p^2 + pq - q^2 \] Therefore: \[ 3p(p - q) - (2p - q)^2 = -p^2 + pq - q^2 \]