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

$$ \begin{aligned} \left( \color{blue}{ 3m+7}\right) \cdot \left( \color{orangered}{ 7m-6}\right) &= \underbrace{ \color{blue}{3m} \cdot \color{orangered}{7m} }_{\text{FIRST}} + \underbrace{ \color{blue}{3m} \cdot \left( \color{orangered}{-6} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{7} \cdot \color{orangered}{7m} }_{\text{INNER}} + \underbrace{ \color{blue}{7} \cdot \left( \color{orangered}{-6} \right) }_{\text{LAST}} = \\ &= 21m^2 + \left( -18m\right) + 49m + \left( -42\right) = \\ &= 21m^2 + \left( -18m\right) + 49m + \left( -42\right) = \\ &= 21m^2+31m-42; \end{aligned} $$

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