Multiply polynomial $ \, \color{blue}{ t-2 } \, $ by $ \, \color{orangered}{ t^2+4 }$.

$$ \left( \color{blue}{t-2} \right) \cdot \left( \color{orangered}{t^2+4} \right) = t^3-2t^2+4t-8 $$

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

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

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