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

$$ \begin{aligned} P(x) &= 5x^4-12x^2 \\ Q(x) &= 2x+5 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ 5x^4-12x^2}\right) \cdot \left( \color{orangered}{ 2x+5}\right) &= \underbrace{ \color{blue}{5x^4} \cdot \color{orangered}{2x} }_{\text{FIRST}} + \underbrace{ \color{blue}{5x^4} \cdot \color{orangered}{5} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-12x^2} \right) \cdot \color{orangered}{2x} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-12x^2} \right) \cdot \color{orangered}{5} }_{\text{LAST}} = \\ &= 10x^5 + 25x^4 + \left( -24x^3\right) + \left( -60x^2\right) = \\ &= 10x^5 + 25x^4 + \left( -24x^3\right) + \left( -60x^2\right) = \\ &= 10x^5+25x^4-24x^3-60x^2; \end{aligned} $$

Polynomial Operations Calculator