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

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Full solution

Q. Find the square. Simplify your answer.\newline(3u−4)2(3u - 4)^2
  1. Identify binomial and formula: Identify the binomial to be squared and the special case formula.\newlineThe given expression is (3u−4)2(3u - 4)^2, which is in the form of (a−b)2(a - b)^2.\newlineSpecial case: (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2
  2. Identify values of aa and bb: Identify the values of aa and bb. Compare (3u−4)2(3u - 4)^2 with (a−b)2(a - b)^2. a=3ua = 3u b=4b = 4
  3. Apply binomial square formula: Apply the square of a binomial formula to expand (3u−4)2(3u - 4)^2.\newline(a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2\newline(3u−4)2=(3u)2−2(3u)(4)+42(3u - 4)^2 = (3u)^2 - 2(3u)(4) + 4^2
  4. Simplify expression: Simplify (3u)2−2(3u)(4)+42.(3u)^2 - 2(3u)(4) + 4^2.(3u)2−2(3u)(4)+42(3u)^2 - 2(3u)(4) + 4^2=(3u⋅3u)−(2⋅3⋅4)u+4⋅4= (3u \cdot 3u) - (2 \cdot 3 \cdot 4)u + 4 \cdot 4=9u2−24u+16= 9u^2 - 24u + 16

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