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Find the square. Simplify your answer. $\newline$ $(3n + 1)^2$

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Multiply two binomials: special cases

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Q. Find the square. Simplify your answer.

\newline

(3n + 1)^2

Identify Binomial & Formula: Identify the binomial to be squared and the special case formula. $\newline$ The given expression is $(3n + 1)^2$ , which is a binomial squared. The special case formula for the square of a binomial $(a + b)^2$ is $a^2 + 2ab + b^2$ .
Identify $a$ and $b$ : Identify the values of $a$ and $b$ in the binomial. $\newline$ In the expression $(3n + 1)^2$ , $a$ is $3n$ and $b$ is $1$ .
Apply Binomial Formula: Apply the square of a binomial formula to expand $(3n + 1)^2$ . Using the formula $(a + b)^2 = a^2 + 2ab + b^2$ , we get: $(3n + 1)^2 = (3n)^2 + 2\cdot(3n)\cdot1 + 1^2$
Simplify Expanded Expression: Simplify the expanded expression. $\newline$ $(3n)^2 + 2\cdot(3n)\cdot 1 + 1^2 = 9n^2 + 6n + 1$

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