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

$$ \begin{aligned} P(x) &= 4x-5 \\ Q(x) &= 3x+3 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ 4x-5}\right) \cdot \left( \color{orangered}{ 3x+3}\right) &= \underbrace{ \color{blue}{4x} \cdot \color{orangered}{3x} }_{\text{FIRST}} + \underbrace{ \color{blue}{4x} \cdot \color{orangered}{3} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-5} \right) \cdot \color{orangered}{3x} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-5} \right) \cdot \color{orangered}{3} }_{\text{LAST}} = \\ &= 12x^2 + 12x + \left( -15x\right) + \left( -15\right) = \\ &= 12x^2 + 12x + \left( -15x\right) + \left( -15\right) = \\ &= 12x^2-3x-15; \end{aligned} $$

Polynomial Operations Calculator