Combine like terms:

$$ \color{blue}{x} \color{blue}{-16x} +93+x^4 = x^4 \color{blue}{-15x} +93 $$

Find $ \left(8x+2\right)^2 $ using formula.

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

where $ A = \color{blue}{ 8x } $ and $ B = \color{red}{ 2 }$.

$$ \begin{aligned}\left(8x+2\right)^2 = \color{blue}{\left( 8x \right)^2} +2 \cdot 8x \cdot 2 + \color{red}{2^2} = 64x^2+32x+4\end{aligned} $$

Multiply each term of $ \left( \color{blue}{3+25x^2}\right) $ by each term in $ \left( 64x^2+32x+4\right) $.

$$ \left( \color{blue}{3+25x^2}\right) \cdot \left( 64x^2+32x+4\right) = 192x^2+96x+12+1600x^4+800x^3+100x^2 $$Multiply $ \color{blue}{2} $ by $ \left( x^4-15x+93\right) $ $$ \color{blue}{2} \cdot \left( x^4-15x+93\right) = 2x^4-30x+186 $$

Combine like terms:

$$ \color{blue}{192x^2} +96x+12+1600x^4+800x^3+ \color{blue}{100x^2} = 1600x^4+800x^3+ \color{blue}{292x^2} +96x+12 $$

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

$$ - \left( 1600x^4+800x^3+292x^2+96x+12 \right) = -1600x^4-800x^3-292x^2-96x-12 $$

Combine like terms:

$$ \color{blue}{888x^4} \color{blue}{-1600x^4} -800x^3-292x^2-96x-12 = \color{blue}{-712x^4} -800x^3-292x^2-96x-12 $$

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

$$ - \left( 2x^4-30x+186 \right) = -2x^4+30x-186 $$

Combine like terms:

$$ \color{blue}{-712x^4} -800x^3-292x^2 \color{red}{-96x} \color{green}{-12} \color{blue}{-2x^4} + \color{red}{30x} \color{green}{-186} = \\ = \color{blue}{-714x^4} -800x^3-292x^2 \color{red}{-66x} \color{green}{-198} $$