Simplify the following: 8 x^2 - 5 x - 7 - (9 x^2 - 3 x - 5) + (x + 7) (x + 1)
-(9 x^2 - 3 x - 5) = -9 x^2 + 3 x + 5:
8 x^2 - 5 x - 7 + -9 x^2 + 3 x + 5 + (x + 7) (x + 1)
(x + 1) (x + 7) = (x) (x) + (x) (7) + (1) (x) + (1) (7) = x^2 + 7 x + x + 7 = x^2 + 8 x + 7:
x^2 + 8 x + 7 + 8 x^2 - 9 x^2 + 3 x - 5 x - 7 + 5
Grouping like terms, 8 x^2 + x^2 - 9 x^2 + 8 x + 3 x - 5 x - 7 + 5 + 7 = (-5 x + 3 x + 8 x) + (8 x^2 - 9 x^2 + x^2) + (-7 + 5 + 7):
(-5 x + 3 x + 8 x) + (8 x^2 - 9 x^2 + x^2) + (-7 + 5 + 7)
-5 x + 3 x + 8 x = 6 x:
6 x + (8 x^2 - 9 x^2 + x^2) + (-7 + 5 + 7)
-7 + 5 + 7 = 5:
6 x + (8 x^2 - 9 x^2 + x^2) + 5
8 x^2 + (x^2 - 9 x^2) = 0:
Answer: 6 x + 5