Multiply polynomial $ \, \color{blue}{ -2x-4x+1 } \, $ by $ \, \color{orangered}{ 4x+9 }$.

$$ \left( \color{blue}{-2x-4x+1} \right) \cdot \left( \color{orangered}{4x+9} \right) = -24x^2-50x+9 $$

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

$$ \begin{aligned} P(x) &= -6x+1 \\ Q(x) &= 4x+9 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ -6x+1}\right) \cdot \left( \color{orangered}{ 4x+9}\right) &= \underbrace{ \left( \color{blue}{-6x} \right) \cdot \color{orangered}{4x} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-6x} \right) \cdot \color{orangered}{9} }_{\text{OUTER}} + \underbrace{ \color{blue}{1} \cdot \color{orangered}{4x} }_{\text{INNER}} + \underbrace{ \color{blue}{1} \cdot \color{orangered}{9} }_{\text{LAST}} = \\ &= -24x^2 + \left( -54x\right) + 4x + 9 = \\ &= -24x^2 + \left( -54x\right) + 4x + 9 = \\ &= -24x^2-50x+9; \end{aligned} $$

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