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

$$ \begin{aligned} P(x) &= -4x+1 \\ Q(x) &= -10x+2 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ -4x+1}\right) \cdot \left( \color{orangered}{ -10x+2}\right) &= \underbrace{ \left( \color{blue}{-4x} \right) \cdot \left( \color{orangered}{-10x} \right) }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-4x} \right) \cdot \color{orangered}{2} }_{\text{OUTER}} + \underbrace{ \color{blue}{1} \cdot \left( \color{orangered}{-10x} \right) }_{\text{INNER}} + \underbrace{ \color{blue}{1} \cdot \color{orangered}{2} }_{\text{LAST}} = \\ &= 40x^2 + \left( -8x\right) + \left( -10x\right) + 2 = \\ &= 40x^2 + \left( -8x\right) + \left( -10x\right) + 2 = \\ &= 40x^2-18x+2; \end{aligned} $$

Polynomial Operations Calculator