Question
Answer
$$(x^2-5)(x^2-7)(x^2-9)=x^6-21x^4+143x^2-315$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2-5)(x^2-7)(x^2-9)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^4-7x^2-5x^2+35)(x^2-9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^4-12x^2+35)(x^2-9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^6-9x^4-12x^4+108x^2+35x^2-315 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^6-21x^4+143x^2-315\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2-5}\right) $ by each term in $ \left( x^2-7\right) $. $$ \left( \color{blue}{x^2-5}\right) \cdot \left( x^2-7\right) = x^4-7x^2-5x^2+35 $$ |
| ② | Combine like terms: $$ x^4 \color{blue}{-7x^2} \color{blue}{-5x^2} +35 = x^4 \color{blue}{-12x^2} +35 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^4-12x^2+35}\right) $ by each term in $ \left( x^2-9\right) $. $$ \left( \color{blue}{x^4-12x^2+35}\right) \cdot \left( x^2-9\right) = x^6-9x^4-12x^4+108x^2+35x^2-315 $$ |
| ④ | Combine like terms: $$ x^6 \color{blue}{-9x^4} \color{blue}{-12x^4} + \color{red}{108x^2} + \color{red}{35x^2} -315 = x^6 \color{blue}{-21x^4} + \color{red}{143x^2} -315 $$ |
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