Answer
$$(jw-5)^4=j^4w^4-20j^3w^3+150j^2w^2-500jw+625$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(jw-5)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}j^4w^4-20j^3w^3+150j^2w^2-500jw+625\end{aligned} $$ | |
| ① | $$ (jw-5)^4 = (jw-5)^2 \cdot (jw-5)^2 $$ |
| ② | Find $ \left(jw-5\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ jw } $ and $ B = \color{red}{ 5 }$. $$ \begin{aligned}\left(jw-5\right)^2 = \color{blue}{\left( jw \right)^2} -2 \cdot jw \cdot 5 + \color{red}{5^2} = j^2w^2-10jw+25\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{j^2w^2-10jw+25}\right) $ by each term in $ \left( j^2w^2-10jw+25\right) $. $$ \left( \color{blue}{j^2w^2-10jw+25}\right) \cdot \left( j^2w^2-10jw+25\right) = \\ = j^4w^4-10j^3w^3+25j^2w^2-10j^3w^3+100j^2w^2-250jw+25j^2w^2-250jw+625 $$ |
| ④ | Combine like terms: $$ j^4w^4 \color{blue}{-10j^3w^3} + \color{red}{25j^2w^2} \color{blue}{-10j^3w^3} + \color{green}{100j^2w^2} \color{orange}{-250jw} + \color{green}{25j^2w^2} \color{orange}{-250jw} +625 = \\ = j^4w^4 \color{blue}{-20j^3w^3} + \color{green}{150j^2w^2} \color{orange}{-500jw} +625 $$ |
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