Question
Answer
$$(2s^2+4s+3)(s^2+8s+4)-(s^2+2s)^2=s^4+16s^3+39s^2+40s+12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2s^2+4s+3)(s^2+8s+4)-(s^2+2s)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2s^2+4s+3)(s^2+8s+4)-(1s^4+4s^3+4s^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2s^4+20s^3+43s^2+40s+12-(1s^4+4s^3+4s^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2s^4+20s^3+43s^2+40s+12-s^4-4s^3-4s^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}s^4+16s^3+39s^2+40s+12\end{aligned} $$ | |
| 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 each term of $ \left( \color{blue}{2s^2+4s+3}\right) $ by each term in $ \left( s^2+8s+4\right) $. $$ \left( \color{blue}{2s^2+4s+3}\right) \cdot \left( s^2+8s+4\right) = 2s^4+16s^3+8s^2+4s^3+32s^2+16s+3s^2+24s+12 $$ |
| ③ | Combine like terms: $$ 2s^4+ \color{blue}{16s^3} + \color{red}{8s^2} + \color{blue}{4s^3} + \color{green}{32s^2} + \color{orange}{16s} + \color{green}{3s^2} + \color{orange}{24s} +12 = \\ = 2s^4+ \color{blue}{20s^3} + \color{green}{43s^2} + \color{orange}{40s} +12 $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( s^4+4s^3+4s^2 \right) = -s^4-4s^3-4s^2 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{2s^4} + \color{red}{20s^3} + \color{green}{43s^2} +40s+12 \color{blue}{-s^4} \color{red}{-4s^3} \color{green}{-4s^2} = \color{blue}{s^4} + \color{red}{16s^3} + \color{green}{39s^2} +40s+12 $$ |
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