Identify Coefficients: Step Title: Identify the CoefficientsConcise Step Description: Identify the coefficients of the quadratic equation, which are the numbers in front of the variables. In this case, the coefficients are 81, −144, and 64.Step Calculation: Coefficients are 81, −144, 64Step Output: Coefficients: 81, −144, 64
Find Factors: Step Title: Find the FactorsConcise Step Description: Find two numbers that multiply to the product of the first and last coefficients (81×64) and add to the middle coefficient (−144).Step Calculation: Factors of 5184 (81×64) that add up to −144 are −72 and −72.Step Output: Factors: −72, −72
Write Factored Form: Step Title: Write the Factored FormConcise Step Description: Write the factored form of the quadratic equation using the factors found in the previous step.Step Calculation: The factored form is (9p−8q)2 because (9p−8q)(9p−8q) gives 81p2−72pq−72pq+64q2, which simplifies to 81p2−144pq+64q2.Step Output: Factored Form: (9p−8q)2