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