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

Identify binomial and formula: Identify the binomial to be squared and the special case formula to use. The binomial to be squared is (3v + 4), and the special case formula for the square of a binomial is (a + b)^2 = a^2 + 2ab + b^2.Determine values of 'a' and 'b': Determine the values of 'a' and 'b' in the binomial. In the expression (3v + 4), 'a' is 3v and 'b' is 4.Apply binomial formula: Apply the square of a binomial formula to expand (3v + 4)^2. Using the formula (a + b)^2 = a^2 + 2ab + b^2, we get (3v + 4)^2 = (3v)^2 + 2*(3v)*(4) + (4)^2.Simplify each term: Simplify each term in the expansion. (3v)^2 = 9v^2, 2*(3v)*(4) = 24v, and (4)^2 = 16. So, (3v + 4)^2 = 9v^2 + 24v + 16.

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

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Math Problems

Algebra 1

Multiply two binomials: special cases

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Q. Find the square. Simplify your answer.

\newline

(3v + 4)^2

Identify binomial and formula: Identify the binomial to be squared and the special case formula to use. $\newline$ The binomial to be squared is $(3v + 4)$ , and the special case formula for the square of a binomial is $(a + b)^2 = a^2 + 2ab + b^2$ .
Determine values of 'a' and 'b': Determine the values of 'a' and 'b' in the binomial. $\newline$ In the expression $(3v + 4)$ , 'a' is $3v$ and 'b' is $4$ .
Apply binomial formula: Apply the square of a binomial formula to expand $(3v + 4)^2$ . Using the formula $(a + b)^2 = a^2 + 2ab + b^2$ , we get $(3v + 4)^2 = (3v)^2 + 2\cdot(3v)\cdot(4) + (4)^2$ .
Simplify each term: Simplify each term in the expansion. $\newline$ $(3v)^2 = 9v^2$ , $2\cdot(3v)\cdot(4) = 24v$ , and $(4)^2 = 16$ . $\newline$ So, $(3v + 4)^2 = 9v^2 + 24v + 16$ .