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

$$ \left( \color{blue}{x-5} \right) \cdot \left( \color{orangered}{x-3} \right) = x^2-8x+15 $$

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

$$ \begin{aligned} \left( \color{blue}{ x-5}\right) \cdot \left( \color{orangered}{ x-3}\right) &= \underbrace{ \color{blue}{x} \cdot \color{orangered}{x} }_{\text{FIRST}} + \underbrace{ \color{blue}{x} \cdot \left( \color{orangered}{-3} \right) }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-5} \right) \cdot \color{orangered}{x} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-5} \right) \cdot \left( \color{orangered}{-3} \right) }_{\text{LAST}} = \\ &= x^2 + \left( -3x\right) + \left( -5x\right) + 15 = \\ &= x^2 + \left( -3x\right) + \left( -5x\right) + 15 = \\ &= x^2-8x+15; \end{aligned} $$

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