Question
Answer
$$(m-5)(m^2+5m+6)=m^3-19m-30$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(m-5)(m^2+5m+6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}m^3+5m^2+6m-5m^2-25m-30 \xlongequal{ } \\[1 em] & \xlongequal{ }m^3+ \cancel{5m^2}+6m -\cancel{5m^2}-25m-30 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}m^3-19m-30\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{m-5}\right) $ by each term in $ \left( m^2+5m+6\right) $. $$ \left( \color{blue}{m-5}\right) \cdot \left( m^2+5m+6\right) = m^3+ \cancel{5m^2}+6m -\cancel{5m^2}-25m-30 $$ |
| ② | Combine like terms: $$ m^3+ \, \color{blue}{ \cancel{5m^2}} \,+ \color{green}{6m} \, \color{blue}{ -\cancel{5m^2}} \, \color{green}{-25m} -30 = m^3 \color{green}{-19m} -30 $$ |
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