Find $ \left(25x-12\right)^2 $ using formula.

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

where $ A = \color{blue}{ 25x } $ and $ B = \color{red}{ 12 }$.

$$ \begin{aligned}\left(25x-12\right)^2 = \color{blue}{\left( 25x \right)^2} -2 \cdot 25x \cdot 12 + \color{red}{12^2} = 625x^2-600x+144\end{aligned} $$

Find $ \left(3x-7\right)^2 $ using formula.

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

where $ A = \color{blue}{ 3x } $ and $ B = \color{red}{ 7 }$.

$$ \begin{aligned}\left(3x-7\right)^2 = \color{blue}{\left( 3x \right)^2} -2 \cdot 3x \cdot 7 + \color{red}{7^2} = 9x^2-42x+49\end{aligned} $$

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

$$ - \left( 625x^2-600x+144 \right) = -625x^2+600x-144 $$

Multiply each term of $ \left( \color{blue}{8x^3-625x^2+600x-144}\right) $ by each term in $ \left( 9x^2-42x+49\right) $.

$$ \left( \color{blue}{8x^3-625x^2+600x-144}\right) \cdot \left( 9x^2-42x+49\right) = \\ = 72x^5-336x^4+392x^3-5625x^4+26250x^3-30625x^2+5400x^3-25200x^2+29400x-1296x^2+6048x-7056 $$

Combine like terms:

$$ 72x^5 \color{blue}{-336x^4} + \color{red}{392x^3} \color{blue}{-5625x^4} + \color{green}{26250x^3} \color{orange}{-30625x^2} + \color{green}{5400x^3} \color{blue}{-25200x^2} + \color{red}{29400x} \color{blue}{-1296x^2} + \color{red}{6048x} -7056 = \\ = 72x^5 \color{blue}{-5961x^4} + \color{green}{32042x^3} \color{blue}{-57121x^2} + \color{red}{35448x} -7056 $$