Find $ \left(x+4\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}{ 4 }$.

$$ \begin{aligned}\left(x+4\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 4 + \color{red}{4^2} = x^2+8x+16\end{aligned} $$

Find $ \left(x+9\right)^3 $ using formula

$$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$

where $ A = x $ and $ B = 9 $.

$$ \left(x+9\right)^3 = x^3+3 \cdot x^2 \cdot 9 + 3 \cdot x \cdot 9^2+9^3 = x^3+27x^2+243x+729 $$

Find $ \left(x+1\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}{ 1 }$.

$$ \begin{aligned}\left(x+1\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 1 + \color{red}{1^2} = x^2+2x+1\end{aligned} $$

Multiply each term of $ \left( \color{blue}{x^2+8x+16}\right) $ by each term in $ \left( x-7\right) $.

$$ \left( \color{blue}{x^2+8x+16}\right) \cdot \left( x-7\right) = x^3-7x^2+8x^2-56x+16x-112 $$

Combine like terms:

$$ x^3 \color{blue}{-7x^2} + \color{blue}{8x^2} \color{red}{-56x} + \color{red}{16x} -112 = x^3+ \color{blue}{x^2} \color{red}{-40x} -112 $$

Multiply each term of $ \left( \color{blue}{x^3+x^2-40x-112}\right) $ by each term in $ \left( x^3+27x^2+243x+729\right) $.

$$ \left( \color{blue}{x^3+x^2-40x-112}\right) \cdot \left( x^3+27x^2+243x+729\right) = \\ = x^6+27x^5+243x^4+729x^3+x^5+27x^4+243x^3+729x^2-40x^4-1080x^3-9720x^2-29160x-112x^3-3024x^2-27216x-81648 $$

Combine like terms:

$$ x^6+ \color{blue}{27x^5} + \color{red}{243x^4} + \color{green}{729x^3} + \color{blue}{x^5} + \color{orange}{27x^4} + \color{blue}{243x^3} + \color{red}{729x^2} \color{orange}{-40x^4} \color{green}{-1080x^3} \color{orange}{-9720x^2} \color{blue}{-29160x} \color{green}{-112x^3} \color{orange}{-3024x^2} \color{blue}{-27216x} -81648 = \\ = x^6+ \color{blue}{28x^5} + \color{orange}{230x^4} \color{green}{-220x^3} \color{orange}{-12015x^2} \color{blue}{-56376x} -81648 $$

Multiply each term of $ \left( \color{blue}{x^6+28x^5+230x^4-220x^3-12015x^2-56376x-81648}\right) $ by each term in $ \left( x^2+2x+1\right) $.

$$ \left( \color{blue}{x^6+28x^5+230x^4-220x^3-12015x^2-56376x-81648}\right) \cdot \left( x^2+2x+1\right) = \\ = x^8+2x^7+x^6+28x^7+56x^6+28x^5+230x^6+460x^5+230x^4-220x^5-440x^4-220x^3-12015x^4-24030x^3-12015x^2-56376x^3-112752x^2-56376x-81648x^2-163296x-81648 $$

Combine like terms:

$$ x^8+ \color{blue}{2x^7} + \color{red}{x^6} + \color{blue}{28x^7} + \color{green}{56x^6} + \color{orange}{28x^5} + \color{green}{230x^6} + \color{blue}{460x^5} + \color{red}{230x^4} \color{blue}{-220x^5} \color{green}{-440x^4} \color{orange}{-220x^3} \color{green}{-12015x^4} \color{blue}{-24030x^3} \color{red}{-12015x^2} \color{blue}{-56376x^3} \color{green}{-112752x^2} \color{orange}{-56376x} \color{green}{-81648x^2} \color{orange}{-163296x} -81648 = \\ = x^8+ \color{blue}{30x^7} + \color{green}{287x^6} + \color{blue}{268x^5} \color{green}{-12225x^4} \color{blue}{-80626x^3} \color{green}{-206415x^2} \color{orange}{-219672x} -81648 $$