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