Question
Answer
$$(a^2+4a+ha+2h+4)(a+2+a+h+2)=2a^3+3a^2h+ah^2+12a^2+12ah+2h^2+24a+12h+16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(a^2+4a+ha+2h+4)(a+2+a+h+2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(a^2+4a+ha+2h+4)(2a+h+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2a^3+3a^2h+ah^2+12a^2+12ah+2h^2+24a+12h+16\end{aligned} $$ | |
| ① | Combine like terms: $$ \color{blue}{a} + \color{red}{2} + \color{blue}{a} +h+ \color{red}{2} = \color{blue}{2a} +h+ \color{red}{4} $$ |
| ② | Multiply each term of $ \left( \color{blue}{a^2+4a+ah+2h+4}\right) $ by each term in $ \left( 2a+h+4\right) $. $$ \left( \color{blue}{a^2+4a+ah+2h+4}\right) \cdot \left( 2a+h+4\right) = \\ = 2a^3+a^2h+4a^2+8a^2+4ah+16a+2a^2h+ah^2+4ah+4ah+2h^2+8h+8a+4h+16 $$ |
| ③ | Combine like terms: $$ 2a^3+ \color{blue}{a^2h} + \color{red}{4a^2} + \color{red}{8a^2} + \color{green}{4ah} + \color{orange}{16a} + \color{blue}{2a^2h} +ah^2+ \color{blue}{4ah} + \color{blue}{4ah} +2h^2+ \color{red}{8h} + \color{orange}{8a} + \color{red}{4h} +16 = \\ = 2a^3+ \color{blue}{3a^2h} +ah^2+ \color{red}{12a^2} + \color{blue}{12ah} +2h^2+ \color{orange}{24a} + \color{red}{12h} +16 $$ |
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