Multiply polynomial $ \, \color{blue}{ 5x^2-3 } \, $ by $ \, \color{orangered}{ x^2-2 }$.

$$ \left( \color{blue}{5x^2-3} \right) \cdot \left( \color{orangered}{x^2-2} \right) = 5x^4-13x^2+6 $$

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

$$ \begin{aligned} \left( \color{blue}{ 5x^2-3}\right) \cdot \left( \color{orangered}{ x^2-2}\right) &= \underbrace{ \color{blue}{5x^2} \cdot \color{orangered}{x^2} }_{\text{FIRST}} + \underbrace{ \color{blue}{5x^2} \cdot \left( \color{orangered}{-2} \right) }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-3} \right) \cdot \color{orangered}{x^2} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-3} \right) \cdot \left( \color{orangered}{-2} \right) }_{\text{LAST}} = \\ &= 5x^4 + \left( -10x^2\right) + \left( -3x^2\right) + 6 = \\ &= 5x^4 + \left( -10x^2\right) + \left( -3x^2\right) + 6 = \\ &= 5x^4-13x^2+6; \end{aligned} $$

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