Question
Answer
$$(5m^2+2n^2-2mn)^2=25m^4-20m^3n+24m^2n^2-8mn^3+4n^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5m^2+2n^2-2mn)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}25m^4-20m^3n+24m^2n^2-8mn^3+4n^4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5m^2+2n^2-2mn}\right) $ by each term in $ \left( 5m^2+2n^2-2mn\right) $. $$ \left( \color{blue}{5m^2+2n^2-2mn}\right) \cdot \left( 5m^2+2n^2-2mn\right) = \\ = 25m^4+10m^2n^2-10m^3n+10m^2n^2+4n^4-4mn^3-10m^3n-4mn^3+4m^2n^2 $$ |
| ② | Combine like terms: $$ 25m^4+ \color{blue}{10m^2n^2} \color{red}{-10m^3n} + \color{green}{10m^2n^2} +4n^4 \color{orange}{-4mn^3} \color{red}{-10m^3n} \color{orange}{-4mn^3} + \color{green}{4m^2n^2} = \\ = 25m^4 \color{red}{-20m^3n} + \color{green}{24m^2n^2} \color{orange}{-8mn^3} +4n^4 $$ |
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