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

$$ \begin{aligned} \left( \color{blue}{ x^2+4}\right) \cdot \left( \color{orangered}{ x^2-6}\right) &= \underbrace{ \color{blue}{x^2} \cdot \color{orangered}{x^2} }_{\text{FIRST}} + \underbrace{ \color{blue}{x^2} \cdot \left( \color{orangered}{-6} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{4} \cdot \color{orangered}{x^2} }_{\text{INNER}} + \underbrace{ \color{blue}{4} \cdot \left( \color{orangered}{-6} \right) }_{\text{LAST}} = \\ &= x^4 + \left( -6x^2\right) + 4x^2 + \left( -24\right) = \\ &= x^4 + \left( -6x^2\right) + 4x^2 + \left( -24\right) = \\ &= x^4-2x^2-24; \end{aligned} $$

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