Question
Answer
$$(a+2)(b+2)(c+2)=abc+2ab+2ac+2bc+4a+4b+4c+8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(a+2)(b+2)(c+2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1ab+2a+2b+4)(c+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}abc+2ab+2ac+2bc+4a+4b+4c+8\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{a+2}\right) $ by each term in $ \left( b+2\right) $. $$ \left( \color{blue}{a+2}\right) \cdot \left( b+2\right) = ab+2a+2b+4 $$ |
| ② | Multiply each term of $ \left( \color{blue}{ab+2a+2b+4}\right) $ by each term in $ \left( c+2\right) $. $$ \left( \color{blue}{ab+2a+2b+4}\right) \cdot \left( c+2\right) = abc+2ab+2ac+4a+2bc+4b+4c+8 $$ |
| ③ | Combine like terms: $$ abc+2ab+2ac+4a+2bc+4b+4c+8 = abc+2ab+2ac+2bc+4a+4b+4c+8 $$ |
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