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

$$ \begin{aligned} \left( \color{blue}{ 4x+3}\right) \cdot \left( \color{orangered}{ x^3-2x^2}\right) &= \underbrace{ \color{blue}{4x} \cdot \color{orangered}{x^3} }_{\text{FIRST}} + \underbrace{ \color{blue}{4x} \cdot \left( \color{orangered}{-2x^2} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{3} \cdot \color{orangered}{x^3} }_{\text{INNER}} + \underbrace{ \color{blue}{3} \cdot \left( \color{orangered}{-2x^2} \right) }_{\text{LAST}} = \\ &= 4x^4 + \left( -8x^3\right) + 3x^3 + \left( -6x^2\right) = \\ &= 4x^4 + \left( -8x^3\right) + 3x^3 + \left( -6x^2\right) = \\ &= 4x^4-5x^3-6x^2; \end{aligned} $$

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