Question
Answer
$$(9q-7t)(5q-t)-(3q-4t)(2q+5t)=39q^2-51qt+27t^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(9q-7t)(5q-t)-(3q-4t)(2q+5t)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}45q^2-9qt-35qt+7t^2-(6q^2+15qt-8qt-20t^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}45q^2-44qt+7t^2-(6q^2+7qt-20t^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}45q^2-44qt+7t^2-6q^2-7qt+20t^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}39q^2-51qt+27t^2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{9q-7t}\right) $ by each term in $ \left( 5q-t\right) $. $$ \left( \color{blue}{9q-7t}\right) \cdot \left( 5q-t\right) = 45q^2-9qt-35qt+7t^2 $$Multiply each term of $ \left( \color{blue}{3q-4t}\right) $ by each term in $ \left( 2q+5t\right) $. $$ \left( \color{blue}{3q-4t}\right) \cdot \left( 2q+5t\right) = 6q^2+15qt-8qt-20t^2 $$ |
| ② | Combine like terms: $$ 45q^2 \color{blue}{-9qt} \color{blue}{-35qt} +7t^2 = 45q^2 \color{blue}{-44qt} +7t^2 $$Combine like terms: $$ 6q^2+ \color{blue}{15qt} \color{blue}{-8qt} -20t^2 = 6q^2+ \color{blue}{7qt} -20t^2 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 6q^2+7qt-20t^2 \right) = -6q^2-7qt+20t^2 $$ |
| ④ | Combine like terms: $$ \color{blue}{45q^2} \color{red}{-44qt} + \color{green}{7t^2} \color{blue}{-6q^2} \color{red}{-7qt} + \color{green}{20t^2} = \color{blue}{39q^2} \color{red}{-51qt} + \color{green}{27t^2} $$ |
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