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