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Factor completely.

81p^(2)-144 pq+64q^(2)=

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Factor completely.\newline81p2144pq+64q2= 81 p^{2}-144 p q+64 q^{2}= \newline \square

Full solution

Q. Factor completely.\newline81p2144pq+64q2= 81 p^{2}-144 p q+64 q^{2}= \newline \square
  1. Identify Coefficients: Step Title: Identify the Coefficients\newlineConcise Step Description: Identify the coefficients of the quadratic equation, which are the numbers in front of the variables. In this case, the coefficients are 8181, 144-144, and 6464.\newlineStep Calculation: Coefficients are 8181, 144-144, 6464\newlineStep Output: Coefficients: 8181, 144-144, 6464
  2. Find Factors: Step Title: Find the Factors\newlineConcise Step Description: Find two numbers that multiply to the product of the first and last coefficients (81×6481\times64) and add to the middle coefficient (144-144).\newlineStep Calculation: Factors of 51845184 (81×6481\times64) that add up to 144-144 are 72-72 and 72-72.\newlineStep Output: Factors: 72-72, 72-72
  3. Write Factored Form: Step Title: Write the Factored Form\newlineConcise Step Description: Write the factored form of the quadratic equation using the factors found in the previous step.\newlineStep Calculation: The factored form is (9p8q)2(9p - 8q)^2 because (9p8q)(9p8q)(9p - 8q)(9p - 8q) gives 81p272pq72pq+64q281p^2 - 72pq - 72pq + 64q^2, which simplifies to 81p2144pq+64q281p^2 - 144pq + 64q^2.\newlineStep Output: Factored Form: (9p8q)2(9p - 8q)^2