\( 1 \leftarrow \)\begin{tabular}{l} Multiply. \\ \( (3 x+7 y)^{2} \) \\ \hline \\ \( \begin{array}{l}(3 x+7 y)^{2}=\square \\ \text { (Simplify your answer.) }\end{array} \)\end{tabular}

Simplify the expression by following steps: - step0: Calculate: \(\left(3x+7y\right)^{2}\) - step1: Calculate: \(9x^{2}+42xy+49y^{2}\) To multiply and simplify \( (3x + 7y)^{2} \), we can use the formula for the square of a binomial, which states that: \[ (a + b)^{2} = a^{2} + 2ab + b^{2} \] In this case, let \( a = 3x \) and \( b = 7y \). Now, applying the formula: 1. Calculate \( a^{2} = (3x)^{2} = 9x^{2} \). 2. Calculate \( b^{2} = (7y)^{2} = 49y^{2} \). 3. Calculate \( 2ab = 2 \cdot (3x) \cdot (7y) = 42xy \). Now, combine all these results: \[ (3x + 7y)^{2} = 9x^{2} + 42xy + 49y^{2} \] Thus, the simplified answer is: \[ (3x + 7y)^{2} = 9x^{2} + 42xy + 49y^{2} \]