Multiply polynomial $ \, \color{blue}{ x+1 } \, $ by $ \, \color{orangered}{ x+1 }$.

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

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

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

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