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

$$ \begin{aligned} \left( \color{blue}{ 3u-3}\right) \cdot \left( \color{orangered}{ 2u+2}\right) &= \underbrace{ \color{blue}{3u} \cdot \color{orangered}{2u} }_{\text{FIRST}} + \underbrace{ \color{blue}{3u} \cdot \color{orangered}{2} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-3} \right) \cdot \color{orangered}{2u} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-3} \right) \cdot \color{orangered}{2} }_{\text{LAST}} = \\ &= 6u^2 + 6u + \left( -6u\right) + \left( -6\right) = \\ &= 6u^2 + 6u + \left( -6u\right) + \left( -6\right) = \\ &= 6u^2-6; \end{aligned} $$

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