-2a(a+b-4)+6(-3a+3a+3b)+b(a+4b-7)
Since - 3 a + 3 a = 0 you can write your expression as:
-2a(a+b-4)+6•3b +b(a+4b-7) =
- 2 a • a - 2 a • b - 2 a • ( - 4 ) + 6 • 3 b + b • a + b • 4 b + b • ( - 7 ) =
- 2 a² - 2 a b + 8 a + 18 b + a b + 4 b² - 7 b =
- 2 a² - 2 a b + a b + 8 a + 18 b - 7 b + 4 b² =
- 2 a² - a b + 8 a + 4 b² + 11 b