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

$$ \begin{aligned} \left( \color{blue}{ 10x^2-2}\right) \cdot \left( \color{orangered}{ 3x+7}\right) &= \underbrace{ \color{blue}{10x^2} \cdot \color{orangered}{3x} }_{\text{FIRST}} + \underbrace{ \color{blue}{10x^2} \cdot \color{orangered}{7} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-2} \right) \cdot \color{orangered}{3x} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-2} \right) \cdot \color{orangered}{7} }_{\text{LAST}} = \\ &= 30x^3 + 70x^2 + \left( -6x\right) + \left( -14\right) = \\ &= 30x^3 + 70x^2 + \left( -6x\right) + \left( -14\right) = \\ &= 30x^3+70x^2-6x-14; \end{aligned} $$

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