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

$$ \begin{aligned} P(x) &= -x^3+2x \\ Q(x) &= -3x^4-7x^2 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ -x^3+2x}\right) \cdot \left( \color{orangered}{ -3x^4-7x^2}\right) &= \underbrace{ \left( \color{blue}{-x^3} \right) \cdot \left( \color{orangered}{-3x^4} \right) }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-x^3} \right) \cdot \left( \color{orangered}{-7x^2} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{2x} \cdot \left( \color{orangered}{-3x^4} \right) }_{\text{INNER}} + \underbrace{ \color{blue}{2x} \cdot \left( \color{orangered}{-7x^2} \right) }_{\text{LAST}} = \\ &= 3x^7 + 7x^5 + \left( -6x^5\right) + \left( -14x^3\right) = \\ &= 3x^7 + 7x^5 + \left( -6x^5\right) + \left( -14x^3\right) = \\ &= 3x^7+x^5-14x^3; \end{aligned} $$

Polynomial Operations Calculator