Rút gọn biểu thức: (2x - 1)^2 + 2(2x - 1)(3x + 1) + (3x + 1)^2

a) To simplify the expression:
(a) (2x-1)^2 +2(2x-1)(3x+1)+(3x+1)^2

First, let's expand each term:
(2x-1)^2 = (2x-1)(2x-1) = 4x^2 - 2x - 2x + 1 = 4x^2 - 4x + 1

2(2x-1)(3x+1) = 2(6x^2 + 2x - 3x - 1) = 12x^2 + 4x - 6x - 2 = 12x^2 - 2x - 2

(3x+1)^2 = (3x+1)(3x+1) = 9x^2 + 3x + 3x + 1 = 9x^2 + 6x + 1

Now, let's combine like terms:
4x^2 - 4x + 1 + 12x^2 - 2x - 2 + 9x^2 + 6x + 1

Combine the x^2 terms: 4x^2 + 12x^2 + 9x^2 = 25x^2
Combine the x terms: -4x - 2x + 6x = 0

Final simplified expression: 25x^2 + 0 + 1 - 2 = 25x^2 - 1

b) To simplify the expression:
(3x-1)^2 -2(9x^2-1)+(3x+1)^2

First, let's expand each term:
(3x-1)^2 = (3x-1)(3x-1) = 9x^2 - 3x - 3x + 1 = 9x^2 - 6x + 1

2(9x^2-1) = 18x^2 - 2

(3x+1)^2 = (3x+1)(3x+1) = 9x^2 + 3x + 3x + 1 = 9x^2 + 6x + 1

Now, let's combine like terms:
9x^2 - 6x + 1 - 18x^2 + 2 + 9x^2 + 6x + 1

Combine the x^2 terms: 9x^2 - 18x^2 + 9x^2 = 0
Combine the x terms: -6x + 6x = 0

Final simplified expression: 0 + 1 + 2 + 1 = 4