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

$$ \begin{aligned} \left( \color{blue}{ 3x+5}\right) \cdot \left( \color{orangered}{ 7x-4}\right) &= \underbrace{ \color{blue}{3x} \cdot \color{orangered}{7x} }_{\text{FIRST}} + \underbrace{ \color{blue}{3x} \cdot \left( \color{orangered}{-4} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{5} \cdot \color{orangered}{7x} }_{\text{INNER}} + \underbrace{ \color{blue}{5} \cdot \left( \color{orangered}{-4} \right) }_{\text{LAST}} = \\ &= 21x^2 + \left( -12x\right) + 35x + \left( -20\right) = \\ &= 21x^2 + \left( -12x\right) + 35x + \left( -20\right) = \\ &= 21x^2+23x-20; \end{aligned} $$

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