Answer
$$(x^2-2)(x^2-7)(x^2-8)=x^6-17x^4+86x^2-112$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2-2)(x^2-7)(x^2-8)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^4-7x^2-2x^2+14)(x^2-8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^4-9x^2+14)(x^2-8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^6-8x^4-9x^4+72x^2+14x^2-112 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^6-17x^4+86x^2-112\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2-2}\right) $ by each term in $ \left( x^2-7\right) $. $$ \left( \color{blue}{x^2-2}\right) \cdot \left( x^2-7\right) = x^4-7x^2-2x^2+14 $$ |
| ② | Combine like terms: $$ x^4 \color{blue}{-7x^2} \color{blue}{-2x^2} +14 = x^4 \color{blue}{-9x^2} +14 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^4-9x^2+14}\right) $ by each term in $ \left( x^2-8\right) $. $$ \left( \color{blue}{x^4-9x^2+14}\right) \cdot \left( x^2-8\right) = x^6-8x^4-9x^4+72x^2+14x^2-112 $$ |
| ④ | Combine like terms: $$ x^6 \color{blue}{-8x^4} \color{blue}{-9x^4} + \color{red}{72x^2} + \color{red}{14x^2} -112 = x^6 \color{blue}{-17x^4} + \color{red}{86x^2} -112 $$ |
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