This is not correct.
To find the cube of (x^2 - 5x - 8), we need to expand it using the formula for cube of a binomial:
(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
In this case, a = x^2 and b = 5x + 8.
Therefore,
(x^2 - 5x - 8)^3 = x^6 - 3x^4(5x - 8) + 3x^2(5x - 8)^2 - (5x - 8)^3
Solving further gives:
x^6 - 15x^5 + 60x^4 - 120x^3 + 120x^2 -48x - 3(5x^2 -8) - 3x^2(10x -16) + 3(25x^2 -80x + 64) - (125x - 200)
So, (x^2 - 5x - 8)^3 = x^6 - 15x^5 + 60x^4 - 120x^3 + 120x^2 -48x - 15x^2 + 24 - 30x^3 + 48x^2 + 75x^2 - 240x + 192 - 125x + 200
Thus, the expanded form of (x^2 - 5x - 8)^3 isx^6 - 15x^5 + 60x^4 - 120x^3 + 120x^2 - 48x - 15x^2 + 24 + 75x^2 - 240x + 192 - 125x + 200
This is not correct.
To find the cube of (x^2 - 5x - 8), we need to expand it using the formula for cube of a binomial:
(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
In this case, a = x^2 and b = 5x + 8.
Therefore,
(x^2 - 5x - 8)^3 = x^6 - 3x^4(5x - 8) + 3x^2(5x - 8)^2 - (5x - 8)^3
Solving further gives:
x^6 - 15x^5 + 60x^4 - 120x^3 + 120x^2 -48x - 3(5x^2 -8) - 3x^2(10x -16) + 3(25x^2 -80x + 64) - (125x - 200)
So, (x^2 - 5x - 8)^3 = x^6 - 15x^5 + 60x^4 - 120x^3 + 120x^2 -48x - 15x^2 + 24 - 30x^3 + 48x^2 + 75x^2 - 240x + 192 - 125x + 200
Thus, the expanded form of (x^2 - 5x - 8)^3 is
x^6 - 15x^5 + 60x^4 - 120x^3 + 120x^2 - 48x - 15x^2 + 24 + 75x^2 - 240x + 192 - 125x + 200