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

$$ \begin{aligned} P(x) &= -4x-2 \\ Q(x) &= 2x+5 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ -4x-2}\right) \cdot \left( \color{orangered}{ 2x+5}\right) &= \underbrace{ \left( \color{blue}{-4x} \right) \cdot \color{orangered}{2x} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-4x} \right) \cdot \color{orangered}{5} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-2} \right) \cdot \color{orangered}{2x} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-2} \right) \cdot \color{orangered}{5} }_{\text{LAST}} = \\ &= -8x^2 + \left( -20x\right) + \left( -4x\right) + \left( -10\right) = \\ &= -8x^2 + \left( -20x\right) + \left( -4x\right) + \left( -10\right) = \\ &= -8x^2-24x-10; \end{aligned} $$

Polynomial Operations Calculator