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Find the square. Simplify your answer.\newline(4h−3)2(4h - 3)^2

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Full solution

Q. Find the square. Simplify your answer.\newline(4h−3)2(4h - 3)^2
  1. Identify Binomial Form: We need to find the square of the binomial (4h−3)(4h - 3). This is in the form of (a−b)2(a - b)^2, which is a special case of binomial expansion.\newlineSpecial case: (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2
  2. Determine aa and bb: Identify the values of aa and bb in the binomial (4h−3)(4h - 3). Compare (4h−3)2(4h - 3)^2 with (a−b)2(a - b)^2. a=4ha = 4h b=3b = 3
  3. Apply Binomial Expansion: Apply the square of a binomial formula to expand (4h−3)2(4h - 3)^2.\newline(a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2\newline(4h−3)2=(4h)2−2(4h)(3)+(3)2(4h - 3)^2 = (4h)^2 - 2(4h)(3) + (3)^2
  4. Simplify Terms: Simplify each term in the expansion.\newline(4h)2−2(4h)(3)+(3)2(4h)^2 - 2(4h)(3) + (3)^2\newline= (4h⋅4h)−(2⋅4⋅3)h+(3⋅3)(4h \cdot 4h) - (2 \cdot 4 \cdot 3)h + (3 \cdot 3)\newline= 16h2−24h+916h^2 - 24h + 9

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