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

$$ \begin{aligned} \left( \color{blue}{ 5x-9}\right) \cdot \left( \color{orangered}{ 5x+9}\right) &= \underbrace{ \color{blue}{5x} \cdot \color{orangered}{5x} }_{\text{FIRST}} + \underbrace{ \color{blue}{5x} \cdot \color{orangered}{9} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-9} \right) \cdot \color{orangered}{5x} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-9} \right) \cdot \color{orangered}{9} }_{\text{LAST}} = \\ &= 25x^2 + 45x + \left( -45x\right) + \left( -81\right) = \\ &= 25x^2 + 45x + \left( -45x\right) + \left( -81\right) = \\ &= 25x^2-81; \end{aligned} $$

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