Multiply polynomial $ \, \color{blue}{ 4x-3 } \, $ by $ \, \color{orangered}{ x^3+2x }$.

$$ \left( \color{blue}{4x-3} \right) \cdot \left( \color{orangered}{x^3+2x} \right) = 4x^4-3x^3+8x^2-6x $$

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

$$ \begin{aligned} \left( \color{blue}{ 4x-3}\right) \cdot \left( \color{orangered}{ x^3+2x}\right) &= \underbrace{ \color{blue}{4x} \cdot \color{orangered}{x^3} }_{\text{FIRST}} + \underbrace{ \color{blue}{4x} \cdot \color{orangered}{2x} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-3} \right) \cdot \color{orangered}{x^3} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-3} \right) \cdot \color{orangered}{2x} }_{\text{LAST}} = \\ &= 4x^4 + 8x^2 + \left( -3x^3\right) + \left( -6x\right) = \\ &= 4x^4 + 8x^2 + \left( -3x^3\right) + \left( -6x\right) = \\ &= 4x^4-3x^3+8x^2-6x; \end{aligned} $$

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