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

$$ \begin{aligned} \left( \color{blue}{ 2x+1}\right) \cdot \left( \color{orangered}{ -4x-3}\right) &= \underbrace{ \color{blue}{2x} \cdot \left( \color{orangered}{-4x} \right) }_{\text{FIRST}} + \underbrace{ \color{blue}{2x} \cdot \left( \color{orangered}{-3} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{1} \cdot \left( \color{orangered}{-4x} \right) }_{\text{INNER}} + \underbrace{ \color{blue}{1} \cdot \left( \color{orangered}{-3} \right) }_{\text{LAST}} = \\ &= -8x^2 + \left( -6x\right) + \left( -4x\right) + \left( -3\right) = \\ &= -8x^2 + \left( -6x\right) + \left( -4x\right) + \left( -3\right) = \\ &= -8x^2-10x-3; \end{aligned} $$

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