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

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

Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= 2x-1 \\ Q(x) &= x-1 \\ \end{aligned} $$

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

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

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