In this example we are multiplying two binomials so FOIL method can be used.

$$ \begin{aligned} \left( \color{blue}{ 3m+1}\right) \cdot \left( \color{orangered}{ m+9}\right) &= \underbrace{ \color{blue}{3m} \cdot \color{orangered}{m} }_{\text{FIRST}} + \underbrace{ \color{blue}{3m} \cdot \color{orangered}{9} }_{\text{OUTER}} + \underbrace{ \color{blue}{1} \cdot \color{orangered}{m} }_{\text{INNER}} + \underbrace{ \color{blue}{1} \cdot \color{orangered}{9} }_{\text{LAST}} = \\ &= 3m^2 + 27m + m + 9 = \\ &= 3m^2 + 27m + m + 9 = \\ &= 3m^2+28m+9; \end{aligned} $$

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