Answer:
(-(8 x^2 - 15 x - 1))
Explanation:
Simplify the following:
(x + 3)^2 - 9 (x - 1)^2 - 9 x + 1
(x + 3) (x + 3) = (x) (x) + (x) (3) + (3) (x) + (3) (3) = x^2 + 3 x + 3 x + 9 = x^2 + 6 x + 9:
(x^2 + 6 x + 9) - 9 (x - 1)^2 - 9 x + 1
(x - 1) (x - 1) = (x) (x) + (x) (-1) + (-1) (x) + (-1) (-1) = x^2 - x - x + 1 = x^2 - 2 x + 1:
9 + 6 x + x^2 - 9(x^2 - 2 x + 1) - 9 x + 1
Grouping like terms, 9 + 6 x + x^2 - 9 (x^2 - 2 x + 1) - 9 x + 1 = -9 (x^2 - 2 x + 1) + x^2 + (6 x - 9 x) + (9 + 1):
-9 (x^2 - 2 x + 1) + x^2 + (6 x - 9 x) + (9 + 1)
6 x - 9 x = -3 x:
-9 (x^2 - 2 x + 1) + x^2 + -3 x + (9 + 1)
9 + 1 = 10:
-9 (x^2 - 2 x + 1) + x^2 - 3 x + 10
-9 (x^2 - 2 x + 1) = -9 x^2 + 18 x - 9:
(-9 x^2 + 18 x - 9) + x^2 - 3 x + 10
Grouping like terms, x^2 - 9 x^2 + 18 x - 3 x - 9 + 10 = (-9 x^2 + x^2) + (18 x - 3 x) + (-9 + 10):
((-9 x^2 + x^2) + (18 x - 3 x) + (-9 + 10))
x^2 - 9 x^2 = -8 x^2:
-8 x^2 + (18 x - 3 x) + (-9 + 10)
18 x - 3 x = 15 x:
-8 x^2 + 15 x + (-9 + 10)
10 - 9 = 1:
-8 x^2 + 15 x + 1
Factor -1 out of -8 x^2 + 15 x + 1:
Answer: (-(8 x^2 - 15 x - 1))