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

$$ \begin{aligned} \left( \color{blue}{ 8x^3-12x^2}\right) \cdot \left( \color{orangered}{ 4x^3+6x^2}\right) &= \underbrace{ \color{blue}{8x^3} \cdot \color{orangered}{4x^3} }_{\text{FIRST}} + \underbrace{ \color{blue}{8x^3} \cdot \color{orangered}{6x^2} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-12x^2} \right) \cdot \color{orangered}{4x^3} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-12x^2} \right) \cdot \color{orangered}{6x^2} }_{\text{LAST}} = \\ &= 32x^6 + 48x^5 + \left( -48x^5\right) + \left( -72x^4\right) = \\ &= 32x^6 + 48x^5 + \left( -48x^5\right) + \left( -72x^4\right) = \\ &= 32x^6-72x^4; \end{aligned} $$

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