Multiply polynomial $ \, \color{blue}{ 6x+5x-8 } \, $ by $ \, \color{orangered}{ 6x-9 }$.

$$ \left( \color{blue}{6x+5x-8} \right) \cdot \left( \color{orangered}{6x-9} \right) = 66x^2-147x+72 $$

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

$$ \begin{aligned} P(x) &= 11x-8 \\ Q(x) &= 6x-9 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ 11x-8}\right) \cdot \left( \color{orangered}{ 6x-9}\right) &= \underbrace{ \color{blue}{11x} \cdot \color{orangered}{6x} }_{\text{FIRST}} + \underbrace{ \color{blue}{11x} \cdot \left( \color{orangered}{-9} \right) }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-8} \right) \cdot \color{orangered}{6x} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-8} \right) \cdot \left( \color{orangered}{-9} \right) }_{\text{LAST}} = \\ &= 66x^2 + \left( -99x\right) + \left( -48x\right) + 72 = \\ &= 66x^2 + \left( -99x\right) + \left( -48x\right) + 72 = \\ &= 66x^2-147x+72; \end{aligned} $$

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