Question
Answer
$$(s^2+2s)^2+5s(2s^2+4s+3)=s^4+14s^3+24s^2+15s$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(s^2+2s)^2+5s(2s^2+4s+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}s^4+4s^3+4s^2+5s(2s^2+4s+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}s^4+4s^3+4s^2+10s^3+20s^2+15s \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}s^4+14s^3+24s^2+15s\end{aligned} $$ | |
| ① | Find $ \left(s^2+2s\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^2 } $ and $ B = \color{red}{ 2s }$. $$ \begin{aligned}\left(s^2+2s\right)^2 = \color{blue}{\left( s^2 \right)^2} +2 \cdot s^2 \cdot 2s + \color{red}{\left( 2s \right)^2} = s^4+4s^3+4s^2\end{aligned} $$ |
| ② | Multiply $ \color{blue}{5s} $ by $ \left( 2s^2+4s+3\right) $ $$ \color{blue}{5s} \cdot \left( 2s^2+4s+3\right) = 10s^3+20s^2+15s $$ |
| ③ | Combine like terms: $$ s^4+ \color{blue}{4s^3} + \color{red}{4s^2} + \color{blue}{10s^3} + \color{red}{20s^2} +15s = s^4+ \color{blue}{14s^3} + \color{red}{24s^2} +15s $$ |
This page was created using
Simplify polynomials calculator