Multiply polynomial $ \, \color{blue}{ 7x+3 } \, $ by $ \, \color{orangered}{ 5x-6 }$.

$$ \left( \color{blue}{7x+3} \right) \cdot \left( \color{orangered}{5x-6} \right) = 35x^2-27x-18 $$

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

$$ \begin{aligned} \left( \color{blue}{ 7x+3}\right) \cdot \left( \color{orangered}{ 5x-6}\right) &= \underbrace{ \color{blue}{7x} \cdot \color{orangered}{5x} }_{\text{FIRST}} + \underbrace{ \color{blue}{7x} \cdot \left( \color{orangered}{-6} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{3} \cdot \color{orangered}{5x} }_{\text{INNER}} + \underbrace{ \color{blue}{3} \cdot \left( \color{orangered}{-6} \right) }_{\text{LAST}} = \\ &= 35x^2 + \left( -42x\right) + 15x + \left( -18\right) = \\ &= 35x^2 + \left( -42x\right) + 15x + \left( -18\right) = \\ &= 35x^2-27x-18; \end{aligned} $$

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