Multiply polynomial $ \, \color{blue}{ -18x-4x-1 } \, $ by $ \, \color{orangered}{ 5x+10 }$.

$$ \left( \color{blue}{-18x-4x-1} \right) \cdot \left( \color{orangered}{5x+10} \right) = -110x^2-225x-10 $$

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

$$ \begin{aligned} P(x) &= -22x-1 \\ Q(x) &= 5x+10 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ -22x-1}\right) \cdot \left( \color{orangered}{ 5x+10}\right) &= \underbrace{ \left( \color{blue}{-22x} \right) \cdot \color{orangered}{5x} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-22x} \right) \cdot \color{orangered}{10} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-1} \right) \cdot \color{orangered}{5x} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-1} \right) \cdot \color{orangered}{10} }_{\text{LAST}} = \\ &= -110x^2 + \left( -220x\right) + \left( -5x\right) + \left( -10\right) = \\ &= -110x^2 + \left( -220x\right) + \left( -5x\right) + \left( -10\right) = \\ &= -110x^2-225x-10; \end{aligned} $$

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