Question
Answer
$$(16x^5-20x^3+5x)(2x^2-1)=32x^7-56x^5+30x^3-5x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(16x^5-20x^3+5x)(2x^2-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}32x^7-16x^5-40x^5+20x^3+10x^3-5x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}32x^7-56x^5+30x^3-5x\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{16x^5-20x^3+5x}\right) $ by each term in $ \left( 2x^2-1\right) $. $$ \left( \color{blue}{16x^5-20x^3+5x}\right) \cdot \left( 2x^2-1\right) = 32x^7-16x^5-40x^5+20x^3+10x^3-5x $$ |
| ② | Combine like terms: $$ 32x^7 \color{blue}{-16x^5} \color{blue}{-40x^5} + \color{red}{20x^3} + \color{red}{10x^3} -5x = 32x^7 \color{blue}{-56x^5} + \color{red}{30x^3} -5x $$ |
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