Multiply polynomial $ \, \color{blue}{ 6x+4 } \, $ by $ \, \color{orangered}{ x^2-9 }$.

$$ \left( \color{blue}{6x+4} \right) \cdot \left( \color{orangered}{x^2-9} \right) = 6x^3+4x^2-54x-36 $$

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

$$ \begin{aligned} \left( \color{blue}{ 6x+4}\right) \cdot \left( \color{orangered}{ x^2-9}\right) &= \underbrace{ \color{blue}{6x} \cdot \color{orangered}{x^2} }_{\text{FIRST}} + \underbrace{ \color{blue}{6x} \cdot \left( \color{orangered}{-9} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{4} \cdot \color{orangered}{x^2} }_{\text{INNER}} + \underbrace{ \color{blue}{4} \cdot \left( \color{orangered}{-9} \right) }_{\text{LAST}} = \\ &= 6x^3 + \left( -54x\right) + 4x^2 + \left( -36\right) = \\ &= 6x^3 + \left( -54x\right) + 4x^2 + \left( -36\right) = \\ &= 6x^3+4x^2-54x-36; \end{aligned} $$

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