Hoping to rebound from a tough last-second loss to the Broncos, the Bengals flew to Lambeau Field for a Week 2 interconference duel with the Green Bay Packers.  Cincinnati delivered the first score in the opening score as quarterback Carson Palmer completed a 5-yard touchdown pass to wide receiver Laveranues Coles.  The Packers would respond as quarterback Aaron Rodgers completed a 3-yard touchdown pass to wide receiver Donald Driver, followed by running back Ryan Grant getting a 4-yard touchdown run.  In the second quarter, the Bengals tied the game as Palmer got a 1-yard touchdown run. Green Bay would reply with cornerback Charles Woodson returning an interception 37 yards for a touchdown.  Cincinnati would end the half as Palmer completed a 5-yard touchdown pass to wide receiver Chris Henry. The Bengals would take the lead in the third quarter as Palmer completed a 13-yard touchdown pass to wide receiver Chad Ochocinco.  In the fourth quarter, Cincinnati pulled away as kicker Shayne Graham nailed a 40-yard field goal.  Afterwards, the Packers delivered their only response as kicker Mason Crosby got a 45-yard field goal. With the win, the Bengals improved to 1-1. This was the first game the franchise had ever won in Green Bay.
Question: How many yards longer was Carson Palmer's third touchdown pass compared to his first?
Answer: 8