The problem asks to multiply two binomials: $(5r - 9s^2)$ and $(-2c - 6s^2)$. We need to express the result as a polynomial.

1. Problem Description

The problem asks to multiply two binomials: $(5r - 9s^2)$ and $(-2c - 6s^2)$. We need to express the result as a polynomial.

2. Solution Steps

We will use the distributive property (also known as FOIL) to multiply the two binomials.

$(5r - 9s^2)(-2c - 6s^2)$

$= (5r)(-2c) + (5r)(-6s^2) + (-9s^2)(-2c) + (-9s^2)(-6s^2)$

$= -10rc - 30rs^2 + 18cs^2 + 54s^4$

Thus, the expanded polynomial is $-10rc - 30rs^2 + 18cs^2 + 54s^4$.

3. Final Answer

$-10rc - 30rs^2 + 18cs^2 + 54s^4$