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

$$ \begin{aligned} \left( \color{blue}{ -6x+3}\right) \cdot \left( \color{orangered}{ -6x+8}\right) &= \underbrace{ \left( \color{blue}{-6x} \right) \cdot \left( \color{orangered}{-6x} \right) }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-6x} \right) \cdot \color{orangered}{8} }_{\text{OUTER}} + \underbrace{ \color{blue}{3} \cdot \left( \color{orangered}{-6x} \right) }_{\text{INNER}} + \underbrace{ \color{blue}{3} \cdot \color{orangered}{8} }_{\text{LAST}} = \\ &= 36x^2 + \left( -48x\right) + \left( -18x\right) + 24 = \\ &= 36x^2 + \left( -48x\right) + \left( -18x\right) + 24 = \\ &= 36x^2-66x+24; \end{aligned} $$

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