Find $ \left(x+3\right)^2 $ using formula.

$$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$

where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 3 }$.

$$ \begin{aligned}\left(x+3\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 3 + \color{red}{3^2} = x^2+6x+9\end{aligned} $$

Find $ \left(7x-6\right)^2 $ using formula.

$$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$

where $ A = \color{blue}{ 7x } $ and $ B = \color{red}{ 6 }$.

$$ \begin{aligned}\left(7x-6\right)^2 = \color{blue}{\left( 7x \right)^2} -2 \cdot 7x \cdot 6 + \color{red}{6^2} = 49x^2-84x+36\end{aligned} $$

Multiply $ \color{blue}{9} $ by $ \left( 4x-1\right) $ $$ \color{blue}{9} \cdot \left( 4x-1\right) = 36x-9 $$

Multiply each term of $ \left( \color{blue}{36x-9}\right) $ by each term in $ \left( 49x^2-84x+36\right) $.

$$ \left( \color{blue}{36x-9}\right) \cdot \left( 49x^2-84x+36\right) = 1764x^3-3024x^2+1296x-441x^2+756x-324 $$

Combine like terms:

$$ 1764x^3 \color{blue}{-3024x^2} + \color{red}{1296x} \color{blue}{-441x^2} + \color{red}{756x} -324 = 1764x^3 \color{blue}{-3465x^2} + \color{red}{2052x} -324 $$

Remove the parentheses by changing the sign of each term within them.

$$ - \left( 1764x^3-3465x^2+2052x-324 \right) = -1764x^3+3465x^2-2052x+324 $$

Combine like terms:

$$ \color{blue}{x^2} + \color{red}{6x} + \color{green}{9} -1764x^3+ \color{blue}{3465x^2} \color{red}{-2052x} + \color{green}{324} = \\ = -1764x^3+ \color{blue}{3466x^2} \color{red}{-2046x} + \color{green}{333} $$