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

$$ \begin{aligned} \left( \color{blue}{ t+1}\right) \cdot \left( \color{orangered}{ 3t-4}\right) &= \underbrace{ \color{blue}{t} \cdot \color{orangered}{3t} }_{\text{FIRST}} + \underbrace{ \color{blue}{t} \cdot \left( \color{orangered}{-4} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{1} \cdot \color{orangered}{3t} }_{\text{INNER}} + \underbrace{ \color{blue}{1} \cdot \left( \color{orangered}{-4} \right) }_{\text{LAST}} = \\ &= 3t^2 + \left( -4t\right) + 3t + \left( -4\right) = \\ &= 3t^2 + \left( -4t\right) + 3t + \left( -4\right) = \\ &= 3t^2-t-4; \end{aligned} $$

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