Multiply polynomial $ \, \color{blue}{ x-4 } \, $ by $ \, \color{orangered}{ 7x+12 }$.

$$ \left( \color{blue}{x-4} \right) \cdot \left( \color{orangered}{7x+12} \right) = 7x^2-16x-48 $$

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

$$ \begin{aligned} \left( \color{blue}{ x-4}\right) \cdot \left( \color{orangered}{ 7x+12}\right) &= \underbrace{ \color{blue}{x} \cdot \color{orangered}{7x} }_{\text{FIRST}} + \underbrace{ \color{blue}{x} \cdot \color{orangered}{12} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-4} \right) \cdot \color{orangered}{7x} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-4} \right) \cdot \color{orangered}{12} }_{\text{LAST}} = \\ &= 7x^2 + 12x + \left( -28x\right) + \left( -48\right) = \\ &= 7x^2 + 12x + \left( -28x\right) + \left( -48\right) = \\ &= 7x^2-16x-48; \end{aligned} $$

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