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

$$ \begin{aligned} \left( \color{blue}{ 4x^3+5}\right) \cdot \left( \color{orangered}{ 3x^6-8x^2}\right) &= \underbrace{ \color{blue}{4x^3} \cdot \color{orangered}{3x^6} }_{\text{FIRST}} + \underbrace{ \color{blue}{4x^3} \cdot \left( \color{orangered}{-8x^2} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{5} \cdot \color{orangered}{3x^6} }_{\text{INNER}} + \underbrace{ \color{blue}{5} \cdot \left( \color{orangered}{-8x^2} \right) }_{\text{LAST}} = \\ &= 12x^9 + \left( -32x^5\right) + 15x^6 + \left( -40x^2\right) = \\ &= 12x^9 + \left( -32x^5\right) + 15x^6 + \left( -40x^2\right) = \\ &= 12x^9+15x^6-32x^5-40x^2; \end{aligned} $$

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