Question
Multiply polynomial $ \, \color{blue}{ 2m^4+5m^2 } \, $ by $ \, \color{orangered}{ m^3-7m }$.
Answer
$$ \left( \color{blue}{2m^4+5m^2} \right) \cdot \left( \color{orangered}{m^3-7m} \right) = 2m^7-9m^5-35m^3 $$
Explanation
In this example we are multiplying two binomials so FOIL method can be used.
$$ \begin{aligned} \left( \color{blue}{ 2m^4+5m^2}\right) \cdot \left( \color{orangered}{ m^3-7m}\right) &= \underbrace{ \color{blue}{2m^4} \cdot \color{orangered}{m^3} }_{\text{FIRST}} + \underbrace{ \color{blue}{2m^4} \cdot \left( \color{orangered}{-7m} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{5m^2} \cdot \color{orangered}{m^3} }_{\text{INNER}} + \underbrace{ \color{blue}{5m^2} \cdot \left( \color{orangered}{-7m} \right) }_{\text{LAST}} = \\ &= 2m^7 + \left( -14m^5\right) + 5m^5 + \left( -35m^3\right) = \\ &= 2m^7 + \left( -14m^5\right) + 5m^5 + \left( -35m^3\right) = \\ &= 2m^7-9m^5-35m^3; \end{aligned} $$This page was created using
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