Multiply polynomial $ \, \color{blue}{ 3x+1 } \, $ by $ \, \color{orangered}{ 2x-3 }$.

$$ \left( \color{blue}{3x+1} \right) \cdot \left( \color{orangered}{2x-3} \right) = 6x^2-7x-3 $$

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

$$ \begin{aligned} \left( \color{blue}{ 3x+1}\right) \cdot \left( \color{orangered}{ 2x-3}\right) &= \underbrace{ \color{blue}{3x} \cdot \color{orangered}{2x} }_{\text{FIRST}} + \underbrace{ \color{blue}{3x} \cdot \left( \color{orangered}{-3} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{1} \cdot \color{orangered}{2x} }_{\text{INNER}} + \underbrace{ \color{blue}{1} \cdot \left( \color{orangered}{-3} \right) }_{\text{LAST}} = \\ &= 6x^2 + \left( -9x\right) + 2x + \left( -3\right) = \\ &= 6x^2 + \left( -9x\right) + 2x + \left( -3\right) = \\ &= 6x^2-7x-3; \end{aligned} $$

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