Question
Answer
$$10x^4(2x+5)(-x^8+1)=-20x^{13}-50x^{12}+20x^5+50x^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}10x^4(2x+5)(-x^8+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(20x^5+50x^4)(-x^8+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-20x^{13}+20x^5-50x^{12}+50x^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-20x^{13}-50x^{12}+20x^5+50x^4\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{10x^4} $ by $ \left( 2x+5\right) $ $$ \color{blue}{10x^4} \cdot \left( 2x+5\right) = 20x^5+50x^4 $$ |
| ② | Multiply each term of $ \left( \color{blue}{20x^5+50x^4}\right) $ by each term in $ \left( -x^8+1\right) $. $$ \left( \color{blue}{20x^5+50x^4}\right) \cdot \left( -x^8+1\right) = -20x^{13}+20x^5-50x^{12}+50x^4 $$ |
| ③ | Combine like terms: $$ -20x^{13}-50x^{12}+20x^5+50x^4 = -20x^{13}-50x^{12}+20x^5+50x^4 $$ |
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