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

$$ \left( \color{blue}{5b-3} \right) \cdot \left( \color{orangered}{6b-5} \right) = 30b^2-43b+15 $$

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

$$ \begin{aligned} \left( \color{blue}{ 5b-3}\right) \cdot \left( \color{orangered}{ 6b-5}\right) &= \underbrace{ \color{blue}{5b} \cdot \color{orangered}{6b} }_{\text{FIRST}} + \underbrace{ \color{blue}{5b} \cdot \left( \color{orangered}{-5} \right) }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-3} \right) \cdot \color{orangered}{6b} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-3} \right) \cdot \left( \color{orangered}{-5} \right) }_{\text{LAST}} = \\ &= 30b^2 + \left( -25b\right) + \left( -18b\right) + 15 = \\ &= 30b^2 + \left( -25b\right) + \left( -18b\right) + 15 = \\ &= 30b^2-43b+15; \end{aligned} $$

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