Multiply polynomial $ \, \color{blue}{ 10x^2+8x } \, $ by $ \, \color{orangered}{ -9x+3 }$.

$$ \left( \color{blue}{10x^2+8x} \right) \cdot \left( \color{orangered}{-9x+3} \right) = -90x^3-42x^2+24x $$

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

$$ \begin{aligned} \left( \color{blue}{ 10x^2+8x}\right) \cdot \left( \color{orangered}{ -9x+3}\right) &= \underbrace{ \color{blue}{10x^2} \cdot \left( \color{orangered}{-9x} \right) }_{\text{FIRST}} + \underbrace{ \color{blue}{10x^2} \cdot \color{orangered}{3} }_{\text{OUTER}} + \underbrace{ \color{blue}{8x} \cdot \left( \color{orangered}{-9x} \right) }_{\text{INNER}} + \underbrace{ \color{blue}{8x} \cdot \color{orangered}{3} }_{\text{LAST}} = \\ &= -90x^3 + 30x^2 + \left( -72x^2\right) + 24x = \\ &= -90x^3 + 30x^2 + \left( -72x^2\right) + 24x = \\ &= -90x^3-42x^2+24x; \end{aligned} $$

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