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

$$ \begin{aligned} P(x) &= 5x^2+3x \\ Q(x) &= 2x-1 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ 5x^2+3x}\right) \cdot \left( \color{orangered}{ 2x-1}\right) &= \underbrace{ \color{blue}{5x^2} \cdot \color{orangered}{2x} }_{\text{FIRST}} + \underbrace{ \color{blue}{5x^2} \cdot \left( \color{orangered}{-1} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{3x} \cdot \color{orangered}{2x} }_{\text{INNER}} + \underbrace{ \color{blue}{3x} \cdot \left( \color{orangered}{-1} \right) }_{\text{LAST}} = \\ &= 10x^3 + \left( -5x^2\right) + 6x^2 + \left( -3x\right) = \\ &= 10x^3 + \left( -5x^2\right) + 6x^2 + \left( -3x\right) = \\ &= 10x^3+x^2-3x; \end{aligned} $$

Polynomial Operations Calculator