Find $ \left(5+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}{ 5 } $ and $ B = \color{red}{ 8x^2 }$.

$$ \begin{aligned}\left(5+8x^2\right)^2 = \color{blue}{5^2} +2 \cdot 5 \cdot 8x^2 + \color{red}{\left( 8x^2 \right)^2} = 25+80x^2+64x^4\end{aligned} $$

Multiply each term of $ \left( \color{blue}{8x^2+2x-5}\right) $ by each term in $ \left( 8x^2+2x-5\right) $.

$$ \left( \color{blue}{8x^2+2x-5}\right) \cdot \left( 8x^2+2x-5\right) = 64x^4+16x^3-40x^2+16x^3+4x^2-10x-40x^2-10x+25 $$

Combine like terms:

$$ 64x^4+ \color{blue}{16x^3} \color{red}{-40x^2} + \color{blue}{16x^3} + \color{green}{4x^2} \color{orange}{-10x} \color{green}{-40x^2} \color{orange}{-10x} +25 = \\ = 64x^4+ \color{blue}{32x^3} \color{green}{-76x^2} \color{orange}{-20x} +25 $$

Multiply $ \color{blue}{41} $ by $ \left( 25+80x^2+64x^4\right) $ $$ \color{blue}{41} \cdot \left( 25+80x^2+64x^4\right) = 1025+3280x^2+2624x^4 $$Multiply $ \color{blue}{40} $ by $ \left( 64x^4+32x^3-76x^2-20x+25\right) $ $$ \color{blue}{40} \cdot \left( 64x^4+32x^3-76x^2-20x+25\right) = 2560x^4+1280x^3-3040x^2-800x+1000 $$

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

$$ - \left( 2560x^4+1280x^3-3040x^2-800x+1000 \right) = -2560x^4-1280x^3+3040x^2+800x-1000 $$

Combine like terms:

$$ \color{blue}{1025} + \color{red}{3280x^2} + \color{green}{2624x^4} \color{green}{-2560x^4} -1280x^3+ \color{red}{3040x^2} +800x \color{blue}{-1000} = \\ = \color{green}{64x^4} -1280x^3+ \color{red}{6320x^2} +800x+ \color{blue}{25} $$