Question
Answer
$$(5v-2e)(6v-7e)-(9v-8e)(9v+7e)=70e^2-38ev-51v^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5v-2e)(6v-7e)-(9v-8e)(9v+7e)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}30v^2-35ev-12ev+14e^2-(81v^2+63ev-72ev-56e^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}14e^2-47ev+30v^2-(-56e^2-9ev+81v^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}14e^2-47ev+30v^2+56e^2+9ev-81v^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}70e^2-38ev-51v^2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5v-2e}\right) $ by each term in $ \left( 6v-7e\right) $. $$ \left( \color{blue}{5v-2e}\right) \cdot \left( 6v-7e\right) = 30v^2-35ev-12ev+14e^2 $$Multiply each term of $ \left( \color{blue}{9v-8e}\right) $ by each term in $ \left( 9v+7e\right) $. $$ \left( \color{blue}{9v-8e}\right) \cdot \left( 9v+7e\right) = 81v^2+63ev-72ev-56e^2 $$ |
| ② | Combine like terms: $$ 30v^2 \color{blue}{-35ev} \color{blue}{-12ev} +14e^2 = 14e^2 \color{blue}{-47ev} +30v^2 $$Combine like terms: $$ 81v^2+ \color{blue}{63ev} \color{blue}{-72ev} -56e^2 = -56e^2 \color{blue}{-9ev} +81v^2 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( -56e^2-9ev+81v^2 \right) = 56e^2+9ev-81v^2 $$ |
| ④ | Combine like terms: $$ \color{blue}{14e^2} \color{red}{-47ev} + \color{green}{30v^2} + \color{blue}{56e^2} + \color{red}{9ev} \color{green}{-81v^2} = \color{blue}{70e^2} \color{red}{-38ev} \color{green}{-51v^2} $$ |
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