Question
Answer
$$(s^3+10s^2)(2s+10)-(s^2+10s+16)(3s^2+20s)=-s^4-20s^3-148s^2-320s$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(s^3+10s^2)(2s+10)-(s^2+10s+16)(3s^2+20s)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2s^4+10s^3+20s^3+100s^2-(3s^4+20s^3+30s^3+200s^2+48s^2+320s) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2s^4+30s^3+100s^2-(3s^4+50s^3+248s^2+320s) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2s^4+30s^3+100s^2-3s^4-50s^3-248s^2-320s \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-s^4-20s^3-148s^2-320s\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{s^3+10s^2}\right) $ by each term in $ \left( 2s+10\right) $. $$ \left( \color{blue}{s^3+10s^2}\right) \cdot \left( 2s+10\right) = 2s^4+10s^3+20s^3+100s^2 $$Multiply each term of $ \left( \color{blue}{s^2+10s+16}\right) $ by each term in $ \left( 3s^2+20s\right) $. $$ \left( \color{blue}{s^2+10s+16}\right) \cdot \left( 3s^2+20s\right) = 3s^4+20s^3+30s^3+200s^2+48s^2+320s $$ |
| ② | Combine like terms: $$ 2s^4+ \color{blue}{10s^3} + \color{blue}{20s^3} +100s^2 = 2s^4+ \color{blue}{30s^3} +100s^2 $$Combine like terms: $$ 3s^4+ \color{blue}{20s^3} + \color{blue}{30s^3} + \color{red}{200s^2} + \color{red}{48s^2} +320s = 3s^4+ \color{blue}{50s^3} + \color{red}{248s^2} +320s $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 3s^4+50s^3+248s^2+320s \right) = -3s^4-50s^3-248s^2-320s $$ |
| ④ | Combine like terms: $$ \color{blue}{2s^4} + \color{red}{30s^3} + \color{green}{100s^2} \color{blue}{-3s^4} \color{red}{-50s^3} \color{green}{-248s^2} -320s = \color{blue}{-s^4} \color{red}{-20s^3} \color{green}{-148s^2} -320s $$ |
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