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

$$ \begin{aligned} P(x) &= -40x+175 \\ Q(x) &= 2x+7 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ -40x+175}\right) \cdot \left( \color{orangered}{ 2x+7}\right) &= \underbrace{ \left( \color{blue}{-40x} \right) \cdot \color{orangered}{2x} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-40x} \right) \cdot \color{orangered}{7} }_{\text{OUTER}} + \underbrace{ \color{blue}{175} \cdot \color{orangered}{2x} }_{\text{INNER}} + \underbrace{ \color{blue}{175} \cdot \color{orangered}{7} }_{\text{LAST}} = \\ &= -80x^2 + \left( -280x\right) + 350x + 1225 = \\ &= -80x^2 + \left( -280x\right) + 350x + 1225 = \\ &= -80x^2+70x+1225; \end{aligned} $$

Polynomial Operations Calculator