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

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

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

$$ \begin{aligned} \left( \color{blue}{ -2x+7}\right) \cdot \left( \color{orangered}{ 4x-4}\right) &= \underbrace{ \left( \color{blue}{-2x} \right) \cdot \color{orangered}{4x} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-2x} \right) \cdot \left( \color{orangered}{-4} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{7} \cdot \color{orangered}{4x} }_{\text{INNER}} + \underbrace{ \color{blue}{7} \cdot \left( \color{orangered}{-4} \right) }_{\text{LAST}} = \\ &= -8x^2 + 8x + 28x + \left( -28\right) = \\ &= -8x^2 + 8x + 28x + \left( -28\right) = \\ &= -8x^2+36x-28; \end{aligned} $$

Polynomial Operations Calculator