Question
Answer
$$(3x^2-1)(35x^4-30x^2+3)=105x^6-125x^4+39x^2-3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3x^2-1)(35x^4-30x^2+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}105x^6-90x^4+9x^2-35x^4+30x^2-3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}105x^6-125x^4+39x^2-3\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3x^2-1}\right) $ by each term in $ \left( 35x^4-30x^2+3\right) $. $$ \left( \color{blue}{3x^2-1}\right) \cdot \left( 35x^4-30x^2+3\right) = 105x^6-90x^4+9x^2-35x^4+30x^2-3 $$ |
| ② | Combine like terms: $$ 105x^6 \color{blue}{-90x^4} + \color{red}{9x^2} \color{blue}{-35x^4} + \color{red}{30x^2} -3 = 105x^6 \color{blue}{-125x^4} + \color{red}{39x^2} -3 $$ |
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