Question
Answer
$$(v+4)^4=v^4+16v^3+96v^2+256v+256$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(v+4)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}v^4+16v^3+96v^2+256v+256\end{aligned} $$ | |
| ① | $$ (v+4)^4 = (v+4)^2 \cdot (v+4)^2 $$ |
| ② | Find $ \left(v+4\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}{ 4 }$. $$ \begin{aligned}\left(v+4\right)^2 = \color{blue}{v^2} +2 \cdot v \cdot 4 + \color{red}{4^2} = v^2+8v+16\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{v^2+8v+16}\right) $ by each term in $ \left( v^2+8v+16\right) $. $$ \left( \color{blue}{v^2+8v+16}\right) \cdot \left( v^2+8v+16\right) = v^4+8v^3+16v^2+8v^3+64v^2+128v+16v^2+128v+256 $$ |
| ④ | Combine like terms: $$ v^4+ \color{blue}{8v^3} + \color{red}{16v^2} + \color{blue}{8v^3} + \color{green}{64v^2} + \color{orange}{128v} + \color{green}{16v^2} + \color{orange}{128v} +256 = \\ = v^4+ \color{blue}{16v^3} + \color{green}{96v^2} + \color{orange}{256v} +256 $$ |
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