Question
Answer
$$11k+7+(n-1)(-6k-2)+(n-1)(n+2)(8k+4)=8kn^2+2kn+4n^2+k+2n+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}11k+7+(n-1)(-6k-2)+(n-1)(n+2)(8k+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}11k+7-6kn-2n+6k+2+(1n^2+2n-n-2)(8k+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}11k+7-6kn-2n+6k+2+(1n^2+n-2)(8k+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-6kn+17k-2n+9+(1n^2+n-2)(8k+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-6kn+17k-2n+9+8kn^2+4n^2+8kn+4n-16k-8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}8kn^2+2kn+4n^2+k+2n+1\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{n-1}\right) $ by each term in $ \left( -6k-2\right) $. $$ \left( \color{blue}{n-1}\right) \cdot \left( -6k-2\right) = -6kn-2n+6k+2 $$Multiply each term of $ \left( \color{blue}{n-1}\right) $ by each term in $ \left( n+2\right) $. $$ \left( \color{blue}{n-1}\right) \cdot \left( n+2\right) = n^2+2n-n-2 $$ |
| ② | Combine like terms: $$ n^2+ \color{blue}{2n} \color{blue}{-n} -2 = n^2+ \color{blue}{n} -2 $$ |
| ③ | Combine like terms: $$ \color{blue}{11k} + \color{red}{7} -6kn-2n+ \color{blue}{6k} + \color{red}{2} = -6kn+ \color{blue}{17k} -2n+ \color{red}{9} $$ |
| ④ | Multiply each term of $ \left( \color{blue}{n^2+n-2}\right) $ by each term in $ \left( 8k+4\right) $. $$ \left( \color{blue}{n^2+n-2}\right) \cdot \left( 8k+4\right) = 8kn^2+4n^2+8kn+4n-16k-8 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{-6kn} + \color{red}{17k} \color{green}{-2n} + \color{orange}{9} +8kn^2+4n^2+ \color{blue}{8kn} + \color{green}{4n} \color{red}{-16k} \color{orange}{-8} = \\ = 8kn^2+ \color{blue}{2kn} +4n^2+ \color{red}{k} + \color{green}{2n} + \color{orange}{1} $$ |
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