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

$$ \begin{aligned} P(x) &= 7x+4 \\ Q(x) &= x+1 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ 7x+4}\right) \cdot \left( \color{orangered}{ x+1}\right) &= \underbrace{ \color{blue}{7x} \cdot \color{orangered}{x} }_{\text{FIRST}} + \underbrace{ \color{blue}{7x} \cdot \color{orangered}{1} }_{\text{OUTER}} + \underbrace{ \color{blue}{4} \cdot \color{orangered}{x} }_{\text{INNER}} + \underbrace{ \color{blue}{4} \cdot \color{orangered}{1} }_{\text{LAST}} = \\ &= 7x^2 + 7x + 4x + 4 = \\ &= 7x^2 + 7x + 4x + 4 = \\ &= 7x^2+11x+4; \end{aligned} $$

Polynomial Operations Calculator