Multiply polynomial $ \, \color{blue}{ 2u-u-3 } \, $ by $ \, \color{orangered}{ 6u-5 }$.

$$ \left( \color{blue}{2u-u-3} \right) \cdot \left( \color{orangered}{6u-5} \right) = 6u^2-23u+15 $$

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

$$ \begin{aligned} P(x) &= u-3 \\ Q(x) &= 6u-5 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ u-3}\right) \cdot \left( \color{orangered}{ 6u-5}\right) &= \underbrace{ \color{blue}{u} \cdot \color{orangered}{6u} }_{\text{FIRST}} + \underbrace{ \color{blue}{u} \cdot \left( \color{orangered}{-5} \right) }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-3} \right) \cdot \color{orangered}{6u} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-3} \right) \cdot \left( \color{orangered}{-5} \right) }_{\text{LAST}} = \\ &= 6u^2 + \left( -5u\right) + \left( -18u\right) + 15 = \\ &= 6u^2 + \left( -5u\right) + \left( -18u\right) + 15 = \\ &= 6u^2-23u+15; \end{aligned} $$

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