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Find the square. Simplify your answer.\newline(3u+2)2(3u + 2)^2

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Multiply two binomials: special casesright chevron icon

Full solution

Q. Find the square. Simplify your answer.\newline(3u+2)2(3u + 2)^2
  1. Identify binomial and formula: Identify the binomial to be squared and the special case formula to use.\newlineThe binomial to be squared is 3u+23u + 2, and the special case formula for the square of a binomial a+b)2 is$a2+2ab+b2a + b)^2\ is \$a^2 + 2ab + b^2.
  2. Determine values of a and b: Determine the values of a and b in the binomial.\newlineIn the expression (3u+2)(3u + 2), aa is 3u3u and bb is 22.
  3. Apply binomial formula: Apply the square of a binomial formula to expand (3u+2)2(3u + 2)^2. Using the formula (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2, we get (3u+2)2=(3u)2+2⋅(3u)⋅(2)+(2)2(3u + 2)^2 = (3u)^2 + 2\cdot(3u)\cdot(2) + (2)^2.
  4. Simplify each term: Simplify each term in the expansion.\newline(3u)2=9u2(3u)^2 = 9u^2, 2⋅(3u)⋅(2)=12u2\cdot(3u)\cdot(2) = 12u, and (2)2=4(2)^2 = 4.\newlineSo, (3u+2)2=9u2+12u+4(3u + 2)^2 = 9u^2 + 12u + 4.

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