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

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

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

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

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