Question
Answer
$$(2k^3+9k^2+13k+9)(3k^2+9k+5)=6k^5+45k^4+130k^3+189k^2+146k+45$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2k^3+9k^2+13k+9)(3k^2+9k+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6k^5+45k^4+130k^3+189k^2+146k+45\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2k^3+9k^2+13k+9}\right) $ by each term in $ \left( 3k^2+9k+5\right) $. $$ \left( \color{blue}{2k^3+9k^2+13k+9}\right) \cdot \left( 3k^2+9k+5\right) = \\ = 6k^5+18k^4+10k^3+27k^4+81k^3+45k^2+39k^3+117k^2+65k+27k^2+81k+45 $$ |
| ② | Combine like terms: $$ 6k^5+ \color{blue}{18k^4} + \color{red}{10k^3} + \color{blue}{27k^4} + \color{green}{81k^3} + \color{orange}{45k^2} + \color{green}{39k^3} + \color{blue}{117k^2} + \color{red}{65k} + \color{blue}{27k^2} + \color{red}{81k} +45 = \\ = 6k^5+ \color{blue}{45k^4} + \color{green}{130k^3} + \color{blue}{189k^2} + \color{red}{146k} +45 $$ |
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