Multiply polynomial $ \, \color{blue}{ x-2 } \, $ by $ \, \color{orangered}{ x^3+8 }$.

$$ \left( \color{blue}{x-2} \right) \cdot \left( \color{orangered}{x^3+8} \right) = x^4-2x^3+8x-16 $$

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

$$ \begin{aligned} \left( \color{blue}{ x-2}\right) \cdot \left( \color{orangered}{ x^3+8}\right) &= \underbrace{ \color{blue}{x} \cdot \color{orangered}{x^3} }_{\text{FIRST}} + \underbrace{ \color{blue}{x} \cdot \color{orangered}{8} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-2} \right) \cdot \color{orangered}{x^3} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-2} \right) \cdot \color{orangered}{8} }_{\text{LAST}} = \\ &= x^4 + 8x + \left( -2x^3\right) + \left( -16\right) = \\ &= x^4 + 8x + \left( -2x^3\right) + \left( -16\right) = \\ &= x^4-2x^3+8x-16; \end{aligned} $$

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