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