Combine the like terms -12xy, 9xy and -3xy.

Step-by-step solution

1. 1

   Read the list as a sum. Presenting terms as "$-12xy$, $9xy$ and $-3xy$" is shorthand for adding them, each keeping its own sign:

   $-12xy+9xy-3xy$

2. 2

   Verify they really are like terms. Like terms must have the same variables raised to the same powers. Every term here is a multiple of $x^1y^1$ — no $x^2$, no lone $y$ — so they can be merged. Terms such as $9x^2y$ or $9x$ could not.

3. 3

   Factor the common variable part out. This is what "combining" actually means; it is the distributive law read backwards:

   $-12xy+9xy-3xy=(-12+9-3)\,xy$

   The variable part $xy$ never changes — it does not become $x^2y^2$ or $3xy$.

4. 4

   Add the coefficients left to right.

   $-12+9=-3,\qquad -3-3=-6$

   so the bracket is $-6$ and the expression is $-6xy$.

5. 5

   Check with a numerical substitution. Take $x=2$, $y=5$, so $xy=10$. The original is $-120+90-30=-60$, and the answer gives $-6\cdot 10=-60$. They agree, confirming $-6xy$.