Question
Answer
$$6u(7u+9v)-5u(3v+2u)=32u^2+39uv$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6u(7u+9v)-5u(3v+2u)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}42u^2+54uv-(15uv+10u^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}42u^2+54uv-15uv-10u^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}32u^2+39uv\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{6u} $ by $ \left( 7u+9v\right) $ $$ \color{blue}{6u} \cdot \left( 7u+9v\right) = 42u^2+54uv $$Multiply $ \color{blue}{5u} $ by $ \left( 3v+2u\right) $ $$ \color{blue}{5u} \cdot \left( 3v+2u\right) = 15uv+10u^2 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 15uv+10u^2 \right) = -15uv-10u^2 $$ |
| ③ | Combine like terms: $$ \color{blue}{42u^2} + \color{red}{54uv} \color{red}{-15uv} \color{blue}{-10u^2} = \color{blue}{32u^2} + \color{red}{39uv} $$ |
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