Question
Answer
$$(n+1)(4nk+4k+1)-s(16kn+16k+2)=4kn^2-16kns+8kn-16ks+4k+n-2s+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(n+1)(4nk+4k+1)-s(16kn+16k+2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4kn^2+4kn+n+4kn+4k+1-(16kns+16ks+2s) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4kn^2+8kn+4k+n+1-(16kns+16ks+2s) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4kn^2+8kn+4k+n+1-16kns-16ks-2s \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}4kn^2-16kns+8kn-16ks+4k+n-2s+1\end{aligned} $$ | |
| 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( 16kn+16k+2\right) $ $$ \color{blue}{s} \cdot \left( 16kn+16k+2\right) = 16kns+16ks+2s $$ |
| 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. $$ - \left( 16kns+16ks+2s \right) = -16kns-16ks-2s $$ |
| ④ | Combine like terms: $$ 4kn^2-16kns+8kn-16ks+4k+n-2s+1 = 4kn^2-16kns+8kn-16ks+4k+n-2s+1 $$ |
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