Answer
$$(x+8)(x+2)(x-4)=x^3+6x^2-24x-64$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+8)(x+2)(x-4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+2x+8x+16)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+10x+16)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-4x^2+10x^2-40x+16x-64 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+6x^2-24x-64\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+8}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{x+8}\right) \cdot \left( x+2\right) = x^2+2x+8x+16 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{2x} + \color{blue}{8x} +16 = x^2+ \color{blue}{10x} +16 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+10x+16}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{x^2+10x+16}\right) \cdot \left( x-4\right) = x^3-4x^2+10x^2-40x+16x-64 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-4x^2} + \color{blue}{10x^2} \color{red}{-40x} + \color{red}{16x} -64 = x^3+ \color{blue}{6x^2} \color{red}{-24x} -64 $$ |
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