Question
Answer
$$2(w+1)\cdot3(2w+1)=12w^2+18w+6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(w+1)\cdot3(2w+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2w+2)\cdot3(2w+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(6w+6)(2w+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}12w^2+6w+12w+6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}12w^2+18w+6\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( w+1\right) $ $$ \color{blue}{2} \cdot \left( w+1\right) = 2w+2 $$ |
| ② | $$ \left( \color{blue}{2w+2}\right) \cdot 3 = 6w+6 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{6w+6}\right) $ by each term in $ \left( 2w+1\right) $. $$ \left( \color{blue}{6w+6}\right) \cdot \left( 2w+1\right) = 12w^2+6w+12w+6 $$ |
| ④ | Combine like terms: $$ 12w^2+ \color{blue}{6w} + \color{blue}{12w} +6 = 12w^2+ \color{blue}{18w} +6 $$ |
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