Multiply polynomial $ \, \color{blue}{ 66x^3+120x^2 } \, $ by $ \, \color{orangered}{ 80x^2-24x }$.

$$ \left( \color{blue}{66x^3+120x^2} \right) \cdot \left( \color{orangered}{80x^2-24x} \right) = 5280x^5+8016x^4-2880x^3 $$

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

$$ \begin{aligned} \left( \color{blue}{ 66x^3+120x^2}\right) \cdot \left( \color{orangered}{ 80x^2-24x}\right) &= \underbrace{ \color{blue}{66x^3} \cdot \color{orangered}{80x^2} }_{\text{FIRST}} + \underbrace{ \color{blue}{66x^3} \cdot \left( \color{orangered}{-24x} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{120x^2} \cdot \color{orangered}{80x^2} }_{\text{INNER}} + \underbrace{ \color{blue}{120x^2} \cdot \left( \color{orangered}{-24x} \right) }_{\text{LAST}} = \\ &= 5280x^5 + \left( -1584x^4\right) + 9600x^4 + \left( -2880x^3\right) = \\ &= 5280x^5 + \left( -1584x^4\right) + 9600x^4 + \left( -2880x^3\right) = \\ &= 5280x^5+8016x^4-2880x^3; \end{aligned} $$

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