Question
Answer
$$(x^2-2)(x^2-3)(x^2-6)=x^6-11x^4+36x^2-36$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2-2)(x^2-3)(x^2-6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^4-3x^2-2x^2+6)(x^2-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^4-5x^2+6)(x^2-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^6-6x^4-5x^4+30x^2+6x^2-36 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^6-11x^4+36x^2-36\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2-2}\right) $ by each term in $ \left( x^2-3\right) $. $$ \left( \color{blue}{x^2-2}\right) \cdot \left( x^2-3\right) = x^4-3x^2-2x^2+6 $$ |
| ② | Combine like terms: $$ x^4 \color{blue}{-3x^2} \color{blue}{-2x^2} +6 = x^4 \color{blue}{-5x^2} +6 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^4-5x^2+6}\right) $ by each term in $ \left( x^2-6\right) $. $$ \left( \color{blue}{x^4-5x^2+6}\right) \cdot \left( x^2-6\right) = x^6-6x^4-5x^4+30x^2+6x^2-36 $$ |
| ④ | Combine like terms: $$ x^6 \color{blue}{-6x^4} \color{blue}{-5x^4} + \color{red}{30x^2} + \color{red}{6x^2} -36 = x^6 \color{blue}{-11x^4} + \color{red}{36x^2} -36 $$ |
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