Simplify: (-x^2 - 7x + 10) - (8x^2 + 8x + 8).

- (9 x^2 + 15 x - 2)

Step-by-step explanation:

Simplify the following:

- (8 x^2 + 8 x + 8) - x^2 - 7 x + 10

Factor 8 out of 8 x^2 + 8 x + 8:

-x^2 - 7 x + 10 - 8 (x^2 + x + 1)

-8 (x^2 + x + 1) = - 8 x^2 - 8 x - 8:

-8 x^2 - 8 x - 8 - x^2 - 7 x + 10

Grouping like terms, - x^2 - 8 x^2 - 7 x - 8 x - 8 + 10 = (-x^2 - 8 x^2) + (-7 x - 8 x) + (10 - 8):

(-x^2 - 8 x^2) + (-7 x - 8 x) + (10 - 8)

-x^2 - 8 x^2 = - 9 x^2:

-9 x^2 + (-7 x - 8 x) + (10 - 8)

-7 x - 8 x = - 15 x:

-9 x^2 + - 15 x + (10 - 8)

10 - 8 = 2:

-9 x^2 - 15 x + 2

Factor - 1 out of - 9 x^2 - 15 x + 2:

Answer: - (9 x^2 + 15 x - 2)