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

$$ \begin{aligned} P(x) &= 6s^4+15s^3 \\ Q(x) &= -15s^4+6s^3 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ 6s^4+15s^3}\right) \cdot \left( \color{orangered}{ -15s^4+6s^3}\right) &= \underbrace{ \color{blue}{6s^4} \cdot \left( \color{orangered}{-15s^4} \right) }_{\text{FIRST}} + \underbrace{ \color{blue}{6s^4} \cdot \color{orangered}{6s^3} }_{\text{OUTER}} + \underbrace{ \color{blue}{15s^3} \cdot \left( \color{orangered}{-15s^4} \right) }_{\text{INNER}} + \underbrace{ \color{blue}{15s^3} \cdot \color{orangered}{6s^3} }_{\text{LAST}} = \\ &= -90s^8 + 36s^7 + \left( -225s^7\right) + 90s^6 = \\ &= -90s^8 + 36s^7 + \left( -225s^7\right) + 90s^6 = \\ &= -90s^8-189s^7+90s^6; \end{aligned} $$

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