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

$$ \begin{aligned} \left( \color{blue}{ 8q-3}\right) \cdot \left( \color{orangered}{ 4q+7}\right) &= \underbrace{ \color{blue}{8q} \cdot \color{orangered}{4q} }_{\text{FIRST}} + \underbrace{ \color{blue}{8q} \cdot \color{orangered}{7} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-3} \right) \cdot \color{orangered}{4q} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-3} \right) \cdot \color{orangered}{7} }_{\text{LAST}} = \\ &= 32q^2 + 56q + \left( -12q\right) + \left( -21\right) = \\ &= 32q^2 + 56q + \left( -12q\right) + \left( -21\right) = \\ &= 32q^2+44q-21; \end{aligned} $$

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