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

Question

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

UpStudy AI · Accepted Answer

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:

$$
(3x + 7y)^{2} = 9x^{2} + 42xy + 49y^{2}
$$
$$ (3x + 7y)^2 = 9x^2 + 42xy + 49y^2 $$

\( 1 \leftarrow \)\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}

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