2) 16(x-1)^2 - 49(x+3)^2=0

To solve this equation, we can use the difference of squares formula: a^2 - b^2 = (a+b)(a-b).

16(x-1)^2 - 49(x+3)^2 = 0
(4(x-1))^2 - (7(x+3))^2 = 0
(4(x-1) + 7(x+3))(4(x-1) - 7(x+3)) = 0
(4x - 4 + 7x + 21)(4x - 4 - 7x - 21) = 0
(11x + 17)(-3x - 25) = 0

Setting each factor equal to zero and solving for x:
11x + 17 = 0 or -3x - 25 = 0

For 11x + 17 = 0:
11x = -17
x = -17/11

For -3x - 25 = 0:
-3x = 25
x = -25/3

Therefore, the solutions to the equation are x = -17/11 and x = -25/3.

4) 4x^2 - 25 - (2x-5)(2x+7) = 0

Expanding the equation:
4x^2 - 25 - (4x^2 - 3x + 14x - 35) = 0
4x^2 - 25 - 4x^2 + 3x - 14x + 35 = 0
-11x + 10 = 0

Solving for x:
-11x = -10
x = -10/-11
x = 10/11

Therefore, the solution to the equation is x = 10/11.

8) x^3 - 8 + (2x+5)(x-2) = 0

Expanding the equation:
x^3 - 8 + 2x^2 - 4x + 5x - 10 = 0
x^3 + 2x^2 + x - 18 = 0

There is no simple factorization for this equation, so we can use numerical methods or a graphing calculator to find the solutions.