(3c^2 − 5cd + d^2) − (7c^2 + 4cd − 9d^2) =
1. Drop the parentheses around the first polynomial since they are not needed.
= 3c^2 − 5cd + d^2 − (7c^2 + 4cd − 9d^2)
2. To drop the parentheses around the second polynomial, every sign inside changes.
= 3c^2 − 5cd + d^2 − 7c^2 - 4cd + 9d^2
3. Combine like terms. Like terms have the same variables and exponents.
= 3c^2 - 7c^2 - 5cd - 4cd + d^2 + 9d^2
= -4c^2 - 9cd + 10d^2