Multiply polynomial $ \, \color{blue}{ 3x+7 } \, $ by $ \, \color{orangered}{ 5x-2 }$.

$$ \left( \color{blue}{3x+7} \right) \cdot \left( \color{orangered}{5x-2} \right) = 15x^2+29x-14 $$

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

$$ \begin{aligned} \left( \color{blue}{ 3x+7}\right) \cdot \left( \color{orangered}{ 5x-2}\right) &= \underbrace{ \color{blue}{3x} \cdot \color{orangered}{5x} }_{\text{FIRST}} + \underbrace{ \color{blue}{3x} \cdot \left( \color{orangered}{-2} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{7} \cdot \color{orangered}{5x} }_{\text{INNER}} + \underbrace{ \color{blue}{7} \cdot \left( \color{orangered}{-2} \right) }_{\text{LAST}} = \\ &= 15x^2 + \left( -6x\right) + 35x + \left( -14\right) = \\ &= 15x^2 + \left( -6x\right) + 35x + \left( -14\right) = \\ &= 15x^2+29x-14; \end{aligned} $$

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