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

$$ \begin{aligned} \left( \color{blue}{ 3x^9+10}\right) \cdot \left( \color{orangered}{ 4x^2-7}\right) &= \underbrace{ \color{blue}{3x^9} \cdot \color{orangered}{4x^2} }_{\text{FIRST}} + \underbrace{ \color{blue}{3x^9} \cdot \left( \color{orangered}{-7} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{10} \cdot \color{orangered}{4x^2} }_{\text{INNER}} + \underbrace{ \color{blue}{10} \cdot \left( \color{orangered}{-7} \right) }_{\text{LAST}} = \\ &= 12x^{11} + \left( -21x^9\right) + 40x^2 + \left( -70\right) = \\ &= 12x^{11} + \left( -21x^9\right) + 40x^2 + \left( -70\right) = \\ &= 12x^{11}-21x^9+40x^2-70; \end{aligned} $$

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