#### Answer

$$6x^2 + 17xy - 45y^2$$

#### Work Step by Step

To multiply the two binomials together, we use the FOIL system, where we multiply the first terms, then the outside terms, then the inside terms, and, finally, the last terms:
$$(3x)(2x) + (3x)(9y) + (-5y)(2x) + (-5y)(9y)$$
We now multiply out the terms:
$$6x^2 + 27xy - 10xy - 45y^2$$
Group like terms together:
$$6x^2 + (27xy - 10xy) - 45y^2$$
Combine like terms:
$$6x^2 + 17xy - 45y^2$$