Answer
$$71uv^2u+3uv^2v-5u^6u^2v^4+3u^3v^2v^2u^5=-2u^8v^4+71u^2v^2+3uv^3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}71uv^2u+3uv^2v-5u^6u^2v^4+3u^3v^2v^2u^5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}71u^2v^2+3uv^3-5u^8v^4+3u^8v^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-5u^8v^4+71u^2v^2+3uv^3+3u^8v^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-2u^8v^4+71u^2v^2+3uv^3\end{aligned} $$ | |
| ① | $$ 71 u v^2 u = 71 u^{1 + 1} v^{2} = 71 u^2 v^2 $$$$ 3 u v^2 v = 3 u v^{2 + 1} = 3 u v^3 $$ |
| ② | $$ 5 u^6 u^2 v^4 = 5 u^{6 + 2} v^{4} = 5 u^8 v^4 $$$$ 3 u^3 v^2 v^2 u^5 = 3 u^{3 + 5} v^{2 + 2} = 3 u^8 v^4 $$ |
| ③ | Combine like terms: $$ 71u^2v^2+3uv^3-5u^8v^4 = -5u^8v^4+71u^2v^2+3uv^3 $$ |
| ④ | Combine like terms: $$ \color{blue}{-5u^8v^4} +71u^2v^2+3uv^3+ \color{blue}{3u^8v^4} = \color{blue}{-2u^8v^4} +71u^2v^2+3uv^3 $$ |
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