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