Answer
$$(x+8)(x+1)(x-4)=x^3+5x^2-28x-32$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+8)(x+1)(x-4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+x+8x+8)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+9x+8)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-4x^2+9x^2-36x+8x-32 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+5x^2-28x-32\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+8}\right) $ by each term in $ \left( x+1\right) $. $$ \left( \color{blue}{x+8}\right) \cdot \left( x+1\right) = x^2+x+8x+8 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{x} + \color{blue}{8x} +8 = x^2+ \color{blue}{9x} +8 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+9x+8}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{x^2+9x+8}\right) \cdot \left( x-4\right) = x^3-4x^2+9x^2-36x+8x-32 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-4x^2} + \color{blue}{9x^2} \color{red}{-36x} + \color{red}{8x} -32 = x^3+ \color{blue}{5x^2} \color{red}{-28x} -32 $$ |
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