Rewrite the expression below.

-2a (a + b - 5) + 3 (-5a + 2b) + b (6a + b - 8)

b^2 + 4 a b - 2 b - 2 a^2 + - 5 a

Step-by-step explanation:

Simplify the following:

-2 a (a + b - 5) + 3 (2 b - 5 a) + b (6 a + b - 8)

-2 a (-5 + a + b) = 10 a - 2 a^2 - 2 a b:

10 a - 2 a^2 - 2 a b + 3 (2 b - 5 a) + b (6 a + b - 8)

3 (2 b - 5 a) = 6 b - 15 a:

10 a - 2 a^2 - 2 a b + 6 b - 15 a + b (6 a + b - 8)

b (-8 + 6 a + b) = - 8 b + 6 a b + b^2:

10 a - 2 a^2 - 2 a b - 15 a + 6 b + - 8 b + 6 a b + b^2

Grouping like terms, 10 a - 2 a^2 - 2 a b - 15 a + 6 b - 8 b + 6 a b + b^2 = b^2 + (6 a b - 2 a b) + (6 b - 8 b) - 2 a^2 + (10 a - 15 a):

b^2 + (6 a b - 2 a b) + (6 b - 8 b) - 2 a^2 + (10 a - 15 a)

a b 6 + a b (-2) = 4 a b:

b^2 + 4 a b + (6 b - 8 b) - 2 a^2 + (10 a - 15 a)

6 b - 8 b = - 2 b:

b^2 + 4 a b + - 2 b - 2 a^2 + (10 a - 15 a)

10 a - 15 a = - 5 a:

Answer: b^2 + 4 a b - 2 b - 2 a^2 + - 5 a