Multiply polynomial $ \, \color{blue}{ 2x+5 } \, $ by $ \, \color{orangered}{ 3x-1 }$.

$$ \left( \color{blue}{2x+5} \right) \cdot \left( \color{orangered}{3x-1} \right) = 6x^2+13x-5 $$

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

$$ \begin{aligned} \left( \color{blue}{ 2x+5}\right) \cdot \left( \color{orangered}{ 3x-1}\right) &= \underbrace{ \color{blue}{2x} \cdot \color{orangered}{3x} }_{\text{FIRST}} + \underbrace{ \color{blue}{2x} \cdot \left( \color{orangered}{-1} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{5} \cdot \color{orangered}{3x} }_{\text{INNER}} + \underbrace{ \color{blue}{5} \cdot \left( \color{orangered}{-1} \right) }_{\text{LAST}} = \\ &= 6x^2 + \left( -2x\right) + 15x + \left( -5\right) = \\ &= 6x^2 + \left( -2x\right) + 15x + \left( -5\right) = \\ &= 6x^2+13x-5; \end{aligned} $$

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