Question
Answer
$$(u^2-2uv+4v^2)^2=u^4-4u^3v+12u^2v^2-16uv^3+16v^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(u^2-2uv+4v^2)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}u^4-4u^3v+12u^2v^2-16uv^3+16v^4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{u^2-2uv+4v^2}\right) $ by each term in $ \left( u^2-2uv+4v^2\right) $. $$ \left( \color{blue}{u^2-2uv+4v^2}\right) \cdot \left( u^2-2uv+4v^2\right) = \\ = u^4-2u^3v+4u^2v^2-2u^3v+4u^2v^2-8uv^3+4u^2v^2-8uv^3+16v^4 $$ |
| ② | Combine like terms: $$ u^4 \color{blue}{-2u^3v} + \color{red}{4u^2v^2} \color{blue}{-2u^3v} + \color{green}{4u^2v^2} \color{orange}{-8uv^3} + \color{green}{4u^2v^2} \color{orange}{-8uv^3} +16v^4 = \\ = u^4 \color{blue}{-4u^3v} + \color{green}{12u^2v^2} \color{orange}{-16uv^3} +16v^4 $$ |
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