Question
Answer
$$(-jw)(-jw+1)(-jw+2)(-jw-10)=j^4w^4+7j^3w^3-28j^2w^2+20jw$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-jw)(-jw+1)(-jw+2)(-jw-10)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1j^2w^2-jw)(-jw+2)(-jw-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(-j^3w^3+2j^2w^2+j^2w^2-2jw)(-jw-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(-j^3w^3+3j^2w^2-2jw)(-jw-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}j^4w^4+10j^3w^3-3j^3w^3-30j^2w^2+2j^2w^2+20jw \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}j^4w^4+7j^3w^3-28j^2w^2+20jw\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{-jw} $ by $ \left( -jw+1\right) $ $$ \color{blue}{-jw} \cdot \left( -jw+1\right) = j^2w^2-jw $$ |
| ② | Multiply each term of $ \left( \color{blue}{j^2w^2-jw}\right) $ by each term in $ \left( -jw+2\right) $. $$ \left( \color{blue}{j^2w^2-jw}\right) \cdot \left( -jw+2\right) = -j^3w^3+2j^2w^2+j^2w^2-2jw $$ |
| ③ | Combine like terms: $$ -j^3w^3+ \color{blue}{2j^2w^2} + \color{blue}{j^2w^2} -2jw = -j^3w^3+ \color{blue}{3j^2w^2} -2jw $$ |
| ④ | Multiply each term of $ \left( \color{blue}{-j^3w^3+3j^2w^2-2jw}\right) $ by each term in $ \left( -jw-10\right) $. $$ \left( \color{blue}{-j^3w^3+3j^2w^2-2jw}\right) \cdot \left( -jw-10\right) = j^4w^4+10j^3w^3-3j^3w^3-30j^2w^2+2j^2w^2+20jw $$ |
| ⑤ | Combine like terms: $$ j^4w^4+ \color{blue}{10j^3w^3} \color{blue}{-3j^3w^3} \color{red}{-30j^2w^2} + \color{red}{2j^2w^2} +20jw = j^4w^4+ \color{blue}{7j^3w^3} \color{red}{-28j^2w^2} +20jw $$ |
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