Multiply polynomial $ \, \color{blue}{ 4t+1 } \, $ by $ \, \color{orangered}{ 2t-1 }$.

$$ \left( \color{blue}{4t+1} \right) \cdot \left( \color{orangered}{2t-1} \right) = 8t^2-2t-1 $$

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

$$ \begin{aligned} \left( \color{blue}{ 4t+1}\right) \cdot \left( \color{orangered}{ 2t-1}\right) &= \underbrace{ \color{blue}{4t} \cdot \color{orangered}{2t} }_{\text{FIRST}} + \underbrace{ \color{blue}{4t} \cdot \left( \color{orangered}{-1} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{1} \cdot \color{orangered}{2t} }_{\text{INNER}} + \underbrace{ \color{blue}{1} \cdot \left( \color{orangered}{-1} \right) }_{\text{LAST}} = \\ &= 8t^2 + \left( -4t\right) + 2t + \left( -1\right) = \\ &= 8t^2 + \left( -4t\right) + 2t + \left( -1\right) = \\ &= 8t^2-2t-1; \end{aligned} $$

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