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

$$ \begin{aligned} \left( \color{blue}{ 3x^3+5x}\right) \cdot \left( \color{orangered}{ 2x^3-2x}\right) &= \underbrace{ \color{blue}{3x^3} \cdot \color{orangered}{2x^3} }_{\text{FIRST}} + \underbrace{ \color{blue}{3x^3} \cdot \left( \color{orangered}{-2x} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{5x} \cdot \color{orangered}{2x^3} }_{\text{INNER}} + \underbrace{ \color{blue}{5x} \cdot \left( \color{orangered}{-2x} \right) }_{\text{LAST}} = \\ &= 6x^6 + \left( -6x^4\right) + 10x^4 + \left( -10x^2\right) = \\ &= 6x^6 + \left( -6x^4\right) + 10x^4 + \left( -10x^2\right) = \\ &= 6x^6+4x^4-10x^2; \end{aligned} $$

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