Question
Answer
$$2\cdot(2+h)\cdot(2+h)\cdot(2+h)=2h^3+12h^2+24h+16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2\cdot(2+h)\cdot(2+h)\cdot(2+h)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(4+2h)\cdot(2+h)\cdot(2+h) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(8+4h+4h+2h^2)\cdot(2+h) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(2h^2+8h+8)\cdot(2+h) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}4h^2+2h^3+16h+8h^2+16+8h \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}2h^3+12h^2+24h+16\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( 2+h\right) $ $$ \color{blue}{2} \cdot \left( 2+h\right) = 4+2h $$ |
| ② | Multiply each term of $ \left( \color{blue}{4+2h}\right) $ by each term in $ \left( 2+h\right) $. $$ \left( \color{blue}{4+2h}\right) \cdot \left( 2+h\right) = 8+4h+4h+2h^2 $$ |
| ③ | Combine like terms: $$ 8+ \color{blue}{4h} + \color{blue}{4h} +2h^2 = 2h^2+ \color{blue}{8h} +8 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{2h^2+8h+8}\right) $ by each term in $ \left( 2+h\right) $. $$ \left( \color{blue}{2h^2+8h+8}\right) \cdot \left( 2+h\right) = 4h^2+2h^3+16h+8h^2+16+8h $$ |
| ⑤ | Combine like terms: $$ \color{blue}{4h^2} +2h^3+ \color{red}{16h} + \color{blue}{8h^2} +16+ \color{red}{8h} = 2h^3+ \color{blue}{12h^2} + \color{red}{24h} +16 $$ |
This page was created using
Simplify polynomials calculator