Answer
$$(a+6)(a^2-8a+8)=a^3-2a^2-40a+48$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(a+6)(a^2-8a+8)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}a^3-8a^2+8a+6a^2-48a+48 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}a^3-2a^2-40a+48\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{a+6}\right) $ by each term in $ \left( a^2-8a+8\right) $. $$ \left( \color{blue}{a+6}\right) \cdot \left( a^2-8a+8\right) = a^3-8a^2+8a+6a^2-48a+48 $$ |
| ② | Combine like terms: $$ a^3 \color{blue}{-8a^2} + \color{red}{8a} + \color{blue}{6a^2} \color{red}{-48a} +48 = a^3 \color{blue}{-2a^2} \color{red}{-40a} +48 $$ |
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