Find $ \left(x-4\right)^3 $ using formula

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

where $ A = x $ and $ B = 4 $.

$$ \left(x-4\right)^3 = x^3-3 \cdot x^2 \cdot 4 + 3 \cdot x \cdot 4^2-4^3 = x^3-12x^2+48x-64 $$

Find $ \left(x+4\right)^3 $ using formula

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

where $ A = x $ and $ B = 4 $.

$$ \left(x+4\right)^3 = x^3+3 \cdot x^2 \cdot 4 + 3 \cdot x \cdot 4^2+4^3 = x^3+12x^2+48x+64 $$

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 }$.

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

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^3-12x^2+48x-64}\right) $ by each term in $ \left( x^3+12x^2+48x+64\right) $.

$$ \left( \color{blue}{x^3-12x^2+48x-64}\right) \cdot \left( x^3+12x^2+48x+64\right) = \\ = x^6+ \cancel{12x^5}+48x^4+ \cancel{64x^3} -\cancel{12x^5}-144x^4 -\cancel{576x^3}-768x^2+48x^4+ \cancel{576x^3}+2304x^2+ \cancel{3072x} -\cancel{64x^3}-768x^2 -\cancel{3072x}-4096 $$

Combine like terms:

$$ x^6+ \, \color{blue}{ \cancel{12x^5}} \,+ \color{green}{48x^4} + \, \color{orange}{ \cancel{64x^3}} \, \, \color{blue}{ -\cancel{12x^5}} \, \color{red}{-144x^4} \, \color{green}{ -\cancel{576x^3}} \, \color{blue}{-768x^2} + \color{red}{48x^4} + \, \color{red}{ \cancel{576x^3}} \,+ \color{green}{2304x^2} + \, \color{orange}{ \cancel{3072x}} \, \, \color{red}{ -\cancel{64x^3}} \, \color{green}{-768x^2} \, \color{orange}{ -\cancel{3072x}} \,-4096 = x^6 \color{red}{-48x^4} + \color{green}{768x^2} -4096 $$

Multiply each term of $ \left( \color{blue}{x^6-48x^4+768x^2-4096}\right) $ by each term in $ \left( x^2-2x+1\right) $.

$$ \left( \color{blue}{x^6-48x^4+768x^2-4096}\right) \cdot \left( x^2-2x+1\right) = \\ = x^8-2x^7+x^6-48x^6+96x^5-48x^4+768x^4-1536x^3+768x^2-4096x^2+8192x-4096 $$

Combine like terms:

$$ x^8-2x^7+ \color{blue}{x^6} \color{blue}{-48x^6} +96x^5 \color{red}{-48x^4} + \color{red}{768x^4} -1536x^3+ \color{green}{768x^2} \color{green}{-4096x^2} +8192x-4096 = \\ = x^8-2x^7 \color{blue}{-47x^6} +96x^5+ \color{red}{720x^4} -1536x^3 \color{green}{-3328x^2} +8192x-4096 $$

Multiply each term of $ \left( \color{blue}{x^8-2x^7-47x^6+96x^5+720x^4-1536x^3-3328x^2+8192x-4096}\right) $ by each term in $ \left( x^2+2x+1\right) $.

$$ \left( \color{blue}{x^8-2x^7-47x^6+96x^5+720x^4-1536x^3-3328x^2+8192x-4096}\right) \cdot \left( x^2+2x+1\right) = \\ = x^{10}+ \cancel{2x^9}+x^8 -\cancel{2x^9}-4x^8-2x^7-47x^8-94x^7-47x^6+96x^7+192x^6+96x^5+720x^6+1440x^5+720x^4-1536x^5-3072x^4-1536x^3-3328x^4-6656x^3-3328x^2+8192x^3+16384x^2+ \cancel{8192x}-4096x^2 -\cancel{8192x}-4096 $$

Combine like terms:

$$ \text{ \text{Text Is Too Long To Display} } = \\ = x^{10} \color{orange}{-50x^8} + \color{orange}{865x^6} \color{orange}{-5680x^4} + \color{orange}{8960x^2} -4096 $$