Answer
$$2r(2r+1)-(r+1)(r+5)=3r^2-4r-5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2r(2r+1)-(r+1)(r+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4r^2+2r-(1r^2+5r+r+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4r^2+2r-(1r^2+6r+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4r^2+2r-r^2-6r-5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3r^2-4r-5\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2r} $ by $ \left( 2r+1\right) $ $$ \color{blue}{2r} \cdot \left( 2r+1\right) = 4r^2+2r $$ Multiply each term of $ \left( \color{blue}{r+1}\right) $ by each term in $ \left( r+5\right) $. $$ \left( \color{blue}{r+1}\right) \cdot \left( r+5\right) = r^2+5r+r+5 $$ |
| ② | Combine like terms: $$ r^2+ \color{blue}{5r} + \color{blue}{r} +5 = r^2+ \color{blue}{6r} +5 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( r^2+6r+5 \right) = -r^2-6r-5 $$ |
| ④ | Combine like terms: $$ \color{blue}{4r^2} + \color{red}{2r} \color{blue}{-r^2} \color{red}{-6r} -5 = \color{blue}{3r^2} \color{red}{-4r} -5 $$ |
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