Finding the Difference: (y^2  4y + 9)  (3y^2  6y  9)
This problem asks us to find the difference between two polynomials. Here's how to solve it stepbystep:

Distribute the negative sign: The minus sign in front of the second set of parentheses means we need to multiply each term inside the parentheses by 1.
This gives us: (y^2  4y + 9) + (1 * 3y^2) + (1 * 6y) + (1 * 9)

Simplify: Now, simplify the expression by multiplying the 1:
y^2  4y + 9  3y^2 + 6y + 9

Combine like terms: Combine the terms with the same variable and exponent:
(y^2  3y^2) + (4y + 6y) + (9 + 9)

Final Result: Add the coefficients of the like terms:
2y^2 + 2y + 18
Therefore, the difference between the two polynomials (y^2  4y + 9) and (3y^2  6y  9) is 2y^2 + 2y + 18.