Question
Answer
$$(3u^2-2uv+4v^2)^2=9u^4-12u^3v+28u^2v^2-16uv^3+16v^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3u^2-2uv+4v^2)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}9u^4-12u^3v+28u^2v^2-16uv^3+16v^4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3u^2-2uv+4v^2}\right) $ by each term in $ \left( 3u^2-2uv+4v^2\right) $. $$ \left( \color{blue}{3u^2-2uv+4v^2}\right) \cdot \left( 3u^2-2uv+4v^2\right) = \\ = 9u^4-6u^3v+12u^2v^2-6u^3v+4u^2v^2-8uv^3+12u^2v^2-8uv^3+16v^4 $$ |
| ② | Combine like terms: $$ 9u^4 \color{blue}{-6u^3v} + \color{red}{12u^2v^2} \color{blue}{-6u^3v} + \color{green}{4u^2v^2} \color{orange}{-8uv^3} + \color{green}{12u^2v^2} \color{orange}{-8uv^3} +16v^4 = \\ = 9u^4 \color{blue}{-12u^3v} + \color{green}{28u^2v^2} \color{orange}{-16uv^3} +16v^4 $$ |
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