Question
Answer
$$(2s+1)(n(8k+4)+4k+3)-(8kn^2+2kn+4n^2+k+2n+1)=-8kn^2+16kns+6kn+8ks-4n^2+8ns+3k+2n+6s+2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2s+1)(n(8k+4)+4k+3)-(8kn^2+2kn+4n^2+k+2n+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2s+1)(8kn+4n+4k+3)-(8kn^2+2kn+4n^2+k+2n+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}16kns+8kn+8ks+8ns+4k+4n+6s+3-(8kn^2+2kn+4n^2+k+2n+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}16kns+8kn+8ks+8ns+4k+4n+6s+3-8kn^2-2kn-4n^2-k-2n-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-8kn^2+16kns+6kn+8ks-4n^2+8ns+3k+2n+6s+2\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{n} $ by $ \left( 8k+4\right) $ $$ \color{blue}{n} \cdot \left( 8k+4\right) = 8kn+4n $$ |
| ② | Multiply each term of $ \left( \color{blue}{2s+1}\right) $ by each term in $ \left( 8kn+4n+4k+3\right) $. $$ \left( \color{blue}{2s+1}\right) \cdot \left( 8kn+4n+4k+3\right) = 16kns+8ns+8ks+6s+8kn+4n+4k+3 $$ |
| ③ | Combine like terms: $$ 16kns+8ns+8ks+6s+8kn+4n+4k+3 = 16kns+8kn+8ks+8ns+4k+4n+6s+3 $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 8kn^2+2kn+4n^2+k+2n+1 \right) = -8kn^2-2kn-4n^2-k-2n-1 $$ |
| ⑤ | Combine like terms: $$ 16kns+ \color{blue}{8kn} +8ks+8ns+ \color{red}{4k} + \color{green}{4n} +6s+ \color{orange}{3} -8kn^2 \color{blue}{-2kn} -4n^2 \color{red}{-k} \color{green}{-2n} \color{orange}{-1} = \\ = -8kn^2+16kns+ \color{blue}{6kn} +8ks-4n^2+8ns+ \color{red}{3k} + \color{green}{2n} +6s+ \color{orange}{2} $$ |
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