Answer
$$(x^3+27)(x^3-1)=x^6+26x^3-27$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^3+27)(x^3-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^6-x^3+27x^3-27 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^6+26x^3-27\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^3+27}\right) $ by each term in $ \left( x^3-1\right) $. $$ \left( \color{blue}{x^3+27}\right) \cdot \left( x^3-1\right) = x^6-x^3+27x^3-27 $$ |
| ② | Combine like terms: $$ x^6 \color{blue}{-x^3} + \color{blue}{27x^3} -27 = x^6+ \color{blue}{26x^3} -27 $$ |
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