Question
Answer
$$(v-25)^4=v^4-100v^3+3750v^2-62500v+390625$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(v-25)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}v^4-100v^3+3750v^2-62500v+390625\end{aligned} $$ | |
| ① | $$ (v-25)^4 = (v-25)^2 \cdot (v-25)^2 $$ |
| ② | Find $ \left(v-25\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ v } $ and $ B = \color{red}{ 25 }$. $$ \begin{aligned}\left(v-25\right)^2 = \color{blue}{v^2} -2 \cdot v \cdot 25 + \color{red}{25^2} = v^2-50v+625\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{v^2-50v+625}\right) $ by each term in $ \left( v^2-50v+625\right) $. $$ \left( \color{blue}{v^2-50v+625}\right) \cdot \left( v^2-50v+625\right) = \\ = v^4-50v^3+625v^2-50v^3+2500v^2-31250v+625v^2-31250v+390625 $$ |
| ④ | Combine like terms: $$ v^4 \color{blue}{-50v^3} + \color{red}{625v^2} \color{blue}{-50v^3} + \color{green}{2500v^2} \color{orange}{-31250v} + \color{green}{625v^2} \color{orange}{-31250v} +390625 = \\ = v^4 \color{blue}{-100v^3} + \color{green}{3750v^2} \color{orange}{-62500v} +390625 $$ |
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