Question
Answer
$$(u^2-uv+3v^2)^2=u^4-2u^3v+7u^2v^2-6uv^3+9v^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(u^2-uv+3v^2)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}u^4-2u^3v+7u^2v^2-6uv^3+9v^4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{u^2-uv+3v^2}\right) $ by each term in $ \left( u^2-uv+3v^2\right) $. $$ \left( \color{blue}{u^2-uv+3v^2}\right) \cdot \left( u^2-uv+3v^2\right) = \\ = u^4-u^3v+3u^2v^2-u^3v+u^2v^2-3uv^3+3u^2v^2-3uv^3+9v^4 $$ |
| ② | Combine like terms: $$ u^4 \color{blue}{-u^3v} + \color{red}{3u^2v^2} \color{blue}{-u^3v} + \color{green}{u^2v^2} \color{orange}{-3uv^3} + \color{green}{3u^2v^2} \color{orange}{-3uv^3} +9v^4 = \\ = u^4 \color{blue}{-2u^3v} + \color{green}{7u^2v^2} \color{orange}{-6uv^3} +9v^4 $$ |
This page was created using
Simplify polynomials calculator