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

$$ \left( \color{blue}{5a+2} \right) \cdot \left( \color{orangered}{2a-3} \right) = 10a^2-11a-6 $$

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

$$ \begin{aligned} \left( \color{blue}{ 5a+2}\right) \cdot \left( \color{orangered}{ 2a-3}\right) &= \underbrace{ \color{blue}{5a} \cdot \color{orangered}{2a} }_{\text{FIRST}} + \underbrace{ \color{blue}{5a} \cdot \left( \color{orangered}{-3} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{2} \cdot \color{orangered}{2a} }_{\text{INNER}} + \underbrace{ \color{blue}{2} \cdot \left( \color{orangered}{-3} \right) }_{\text{LAST}} = \\ &= 10a^2 + \left( -15a\right) + 4a + \left( -6\right) = \\ &= 10a^2 + \left( -15a\right) + 4a + \left( -6\right) = \\ &= 10a^2-11a-6; \end{aligned} $$

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