Question
Answer
$$s(s+2)((s+2)^2+1)=s^4+6s^3+13s^2+10s$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}s(s+2)((s+2)^2+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}s(s+2)(1s^2+4s+4+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}s(s+2)(1s^2+4s+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(1s^2+2s)(1s^2+4s+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}s^4+4s^3+5s^2+2s^3+8s^2+10s \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}s^4+6s^3+13s^2+10s\end{aligned} $$ | |
| ① | Find $ \left(s+2\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ s } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(s+2\right)^2 = \color{blue}{s^2} +2 \cdot s \cdot 2 + \color{red}{2^2} = s^2+4s+4\end{aligned} $$ |
| ② | Combine like terms: $$ s^2+4s+ \color{blue}{4} + \color{blue}{1} = s^2+4s+ \color{blue}{5} $$ |
| ③ | Multiply $ \color{blue}{s} $ by $ \left( s+2\right) $ $$ \color{blue}{s} \cdot \left( s+2\right) = s^2+2s $$ |
| ④ | Multiply each term of $ \left( \color{blue}{s^2+2s}\right) $ by each term in $ \left( s^2+4s+5\right) $. $$ \left( \color{blue}{s^2+2s}\right) \cdot \left( s^2+4s+5\right) = s^4+4s^3+5s^2+2s^3+8s^2+10s $$ |
| ⑤ | Combine like terms: $$ s^4+ \color{blue}{4s^3} + \color{red}{5s^2} + \color{blue}{2s^3} + \color{red}{8s^2} +10s = s^4+ \color{blue}{6s^3} + \color{red}{13s^2} +10s $$ |
This page was created using
Simplify polynomials calculator