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Find the square. Simplify your answer.\newline(2t3)2(2t - 3)^2

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Q. Find the square. Simplify your answer.\newline(2t3)2(2t - 3)^2
  1. Special Case Identification: We are asked to find the square of the binomial (2t3)(2t - 3). This means we need to calculate (2t3)2(2t - 3)^2. Which special case applies here? (2t3)2(2t - 3)^2 is in the form of (ab)2(a - b)^2. Special case: (ab)2=a22ab+b2(a - b)^2 = a^2 - 2ab + b^2
  2. Values of a and b: Identify the values of aa and bb. Compare (2t3)2(2t - 3)^2 with (ab)2(a - b)^2. a=2ta = 2t b=3b = 3
  3. Application of Formula: Apply the square of a binomial formula to expand (2t3)2(2t - 3)^2.(ab)2=a22ab+b2(a - b)^2 = a^2 - 2ab + b^2(2t3)2=(2t)22(2t)(3)+32(2t - 3)^2 = (2t)^2 - 2(2t)(3) + 3^2
  4. Simplification: Simplify (2t)22(2t)(3)+32.(2t)^2 - 2(2t)(3) + 3^2.(2t)22(2t)(3)+32(2t)^2 - 2(2t)(3) + 3^2=(2t2t)(223)t+33= (2t \cdot 2t) - (2 \cdot 2 \cdot 3)t + 3 \cdot 3=4t212t+9= 4t^2 - 12t + 9

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