SIMPLIFY (−9h^​2 ​​−2hk+6k ^2 ​​)−(5h ^2 ​​+2hk+k^​2 ​​)

Simplify the following:
-9 h^2 - 2 h k + 6 k^2 - (5 h^2 + 2 h k + k^2)

-(5 h^2 + 2 h k + k^2) = -5 h^2 - 2 h k - k^2:
-9 h^2 - 2 h k + 6 k^2 + -5 h^2 - 2 h k - k^2

Grouping like terms, -9 h^2 - 2 h k + 6 k^2 - 5 h^2 - 2 h k - k^2 = (6 k^2 - k^2) + (-2 h k - 2 h k) + (-9 h^2 - 5 h^2):
(6 k^2 - k^2) + (-2 h k - 2 h k) + (-9 h^2 - 5 h^2)

6 k^2 - k^2 = 5 k^2:
5 k^2 + (-2 h k - 2 h k) + (-9 h^2 - 5 h^2)

-2 (h k) - 2 (h k) = -4 (h k):
5 k^2 + -4 h k + (-9 h^2 - 5 h^2)

-9 h^2 - 5 h^2 = -14 h^2:
Answer: |5k^2 - 4hk  -14h^2

It is also much shorter.

simplify (−4a​2​​+3ab+6b​2​​)+(−2a​2​​+2ab−5b​2​​)

 (−4a​^2​​+3ab+6b^​2​​)+(−2a^​2​​+2ab−5b^​2​​)  =

-6a^2 + 5ab + b^2