Question
Answer
$$(2+h)\cdot(2+h)\cdot(2+h)=h^3+6h^2+12h+8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2+h)\cdot(2+h)\cdot(2+h)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(4+2h+2h+h^2)\cdot(2+h) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(1h^2+4h+4)\cdot(2+h) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2h^2+h^3+8h+4h^2+8+4h \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}h^3+6h^2+12h+8\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2+h}\right) $ by each term in $ \left( 2+h\right) $. $$ \left( \color{blue}{2+h}\right) \cdot \left( 2+h\right) = 4+2h+2h+h^2 $$ |
| ② | Combine like terms: $$ 4+ \color{blue}{2h} + \color{blue}{2h} +h^2 = h^2+ \color{blue}{4h} +4 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{h^2+4h+4}\right) $ by each term in $ \left( 2+h\right) $. $$ \left( \color{blue}{h^2+4h+4}\right) \cdot \left( 2+h\right) = 2h^2+h^3+8h+4h^2+8+4h $$ |
| ④ | Combine like terms: $$ \color{blue}{2h^2} +h^3+ \color{red}{8h} + \color{blue}{4h^2} +8+ \color{red}{4h} = h^3+ \color{blue}{6h^2} + \color{red}{12h} +8 $$ |
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