Multiply polynomial $ \, \color{blue}{ 12x+7 } \, $ by $ \, \color{orangered}{ -6x+2 }$.

$$ \left( \color{blue}{12x+7} \right) \cdot \left( \color{orangered}{-6x+2} \right) = -72x^2-18x+14 $$

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

$$ \begin{aligned} \left( \color{blue}{ 12x+7}\right) \cdot \left( \color{orangered}{ -6x+2}\right) &= \underbrace{ \color{blue}{12x} \cdot \left( \color{orangered}{-6x} \right) }_{\text{FIRST}} + \underbrace{ \color{blue}{12x} \cdot \color{orangered}{2} }_{\text{OUTER}} + \underbrace{ \color{blue}{7} \cdot \left( \color{orangered}{-6x} \right) }_{\text{INNER}} + \underbrace{ \color{blue}{7} \cdot \color{orangered}{2} }_{\text{LAST}} = \\ &= -72x^2 + 24x + \left( -42x\right) + 14 = \\ &= -72x^2 + 24x + \left( -42x\right) + 14 = \\ &= -72x^2-18x+14; \end{aligned} $$

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