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

$$ \left( \color{blue}{3x+2} \right) \cdot \left( \color{orangered}{-2x-5} \right) = -6x^2-19x-10 $$

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

$$ \begin{aligned} \left( \color{blue}{ 3x+2}\right) \cdot \left( \color{orangered}{ -2x-5}\right) &= \underbrace{ \color{blue}{3x} \cdot \left( \color{orangered}{-2x} \right) }_{\text{FIRST}} + \underbrace{ \color{blue}{3x} \cdot \left( \color{orangered}{-5} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{2} \cdot \left( \color{orangered}{-2x} \right) }_{\text{INNER}} + \underbrace{ \color{blue}{2} \cdot \left( \color{orangered}{-5} \right) }_{\text{LAST}} = \\ &= -6x^2 + \left( -15x\right) + \left( -4x\right) + \left( -10\right) = \\ &= -6x^2 + \left( -15x\right) + \left( -4x\right) + \left( -10\right) = \\ &= -6x^2-19x-10; \end{aligned} $$

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