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Find the square. Simplify your answer.\newline(3v+4)2(3v + 4)^2

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Full solution

Q. Find the square. Simplify your answer.\newline(3v+4)2(3v + 4)^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 (3v+4)(3v + 4), and the special case formula for the square of a binomial is (a+b)2=a2+2ab+b2(a + b)^2 = 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 (3v+4)(3v + 4), 'a' is 3v3v and 'b' is 44.
  3. Apply binomial formula: Apply the square of a binomial formula to expand (3v+4)2(3v + 4)^2. Using the formula (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2, we get (3v+4)2=(3v)2+2⋅(3v)⋅(4)+(4)2(3v + 4)^2 = (3v)^2 + 2\cdot(3v)\cdot(4) + (4)^2.
  4. Simplify each term: Simplify each term in the expansion.\newline(3v)2=9v2(3v)^2 = 9v^2, 2⋅(3v)⋅(4)=24v2\cdot(3v)\cdot(4) = 24v, and (4)2=16(4)^2 = 16.\newlineSo, (3v+4)2=9v2+24v+16(3v + 4)^2 = 9v^2 + 24v + 16.

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