Multiply polynomial $ \, \color{blue}{ 4x+3 } \, $ by $ \, \color{orangered}{ x^2-5 }$.

$$ \left( \color{blue}{4x+3} \right) \cdot \left( \color{orangered}{x^2-5} \right) = 4x^3+3x^2-20x-15 $$

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

$$ \begin{aligned} \left( \color{blue}{ 4x+3}\right) \cdot \left( \color{orangered}{ x^2-5}\right) &= \underbrace{ \color{blue}{4x} \cdot \color{orangered}{x^2} }_{\text{FIRST}} + \underbrace{ \color{blue}{4x} \cdot \left( \color{orangered}{-5} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{3} \cdot \color{orangered}{x^2} }_{\text{INNER}} + \underbrace{ \color{blue}{3} \cdot \left( \color{orangered}{-5} \right) }_{\text{LAST}} = \\ &= 4x^3 + \left( -20x\right) + 3x^2 + \left( -15\right) = \\ &= 4x^3 + \left( -20x\right) + 3x^2 + \left( -15\right) = \\ &= 4x^3+3x^2-20x-15; \end{aligned} $$

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