Multiply polynomial $ \, \color{blue}{ x^4-81 } \, $ by $ \, \color{orangered}{ x-3 }$.

$$ \left( \color{blue}{x^4-81} \right) \cdot \left( \color{orangered}{x-3} \right) = x^5-3x^4-81x+243 $$

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

$$ \begin{aligned} \left( \color{blue}{ x^4-81}\right) \cdot \left( \color{orangered}{ x-3}\right) &= \underbrace{ \color{blue}{x^4} \cdot \color{orangered}{x} }_{\text{FIRST}} + \underbrace{ \color{blue}{x^4} \cdot \left( \color{orangered}{-3} \right) }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-81} \right) \cdot \color{orangered}{x} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-81} \right) \cdot \left( \color{orangered}{-3} \right) }_{\text{LAST}} = \\ &= x^5 + \left( -3x^4\right) + \left( -81x\right) + 243 = \\ &= x^5 + \left( -3x^4\right) + \left( -81x\right) + 243 = \\ &= x^5-3x^4-81x+243; \end{aligned} $$

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