Multiply polynomial $ \, \color{blue}{ x^2+1 } \, $ by $ \, \color{orangered}{ -x^3+x^2 }$.

$$ \left( \color{blue}{x^2+1} \right) \cdot \left( \color{orangered}{-x^3+x^2} \right) = -x^5+x^4-x^3+x^2 $$

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

$$ \begin{aligned} \left( \color{blue}{ x^2+1}\right) \cdot \left( \color{orangered}{ -x^3+x^2}\right) &= \underbrace{ \color{blue}{x^2} \cdot \left( \color{orangered}{-x^3} \right) }_{\text{FIRST}} + \underbrace{ \color{blue}{x^2} \cdot \color{orangered}{x^2} }_{\text{OUTER}} + \underbrace{ \color{blue}{1} \cdot \left( \color{orangered}{-x^3} \right) }_{\text{INNER}} + \underbrace{ \color{blue}{1} \cdot \color{orangered}{x^2} }_{\text{LAST}} = \\ &= -x^5 + x^4 + \left( -x^3\right) + x^2 = \\ &= -x^5 + x^4 + \left( -x^3\right) + x^2 = \\ &= -x^5+x^4-x^3+x^2; \end{aligned} $$

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