(8x-5)^3 ?

(8x - 5)^3
= (8x - 5)(8x - 5)^2
= (8x - 5)(64x^2 - 80x + 25)
= 512x^3 - 640x^2 + 200x - 320x^2 + 400x - 125
= 512x^3 - 920x^2 + 600x - 125

cube of a binomial
(x-y)^3 = x^3 - 3x^2y +3xy^2 -y^3

thus,
(8x-5)^3 = (8x)^3 - 3(8x)^2 (5) +3(8x)(5)^2 - (5)^3
(8x-5)^3= 512x^3 - 3(64x^2)(5) + 24x(25) - 125
(8x-5)^3= 512x^3 - 960x^2 + 600x -125



(8x-5)^3= 512x^3 - 960x^2 + 600x -125

formula to be used: (a-b)^3 = a^3 - b^3 - 3ab(a-b)
(8x-5)^3 = (8x)^3 - (5)^3 -3(8x)(5)(8x-5)
= 512x^3 - 125 - 120x(8x-5)
= 512x^3 - 125 -960x^2 + 600x

(8x - 5)^3
= (8x - 5)(8x - 5)(8x - 5)
= (8x*8x - 5*8x - 8x*5 + 5*5)(8x - 5)
= (64x^2 - 40x - 40x + 25)(8x - 5)
= (64x^2 - 80x + 25)(8x - 5)
= 64x^2*8x - 80x*8x + 25*8x - 64x^2*5 + 80x*5 - 25*5
= 512x^3 - 640x^2 + 200x - 320x^2 + 400x - 125
= 512x^3 - 640x^2 - 320x^2 + 200x + 400x - 125
= 512x^3 - 960x^2 + 600x - 125

(8x-5)(8x-5)(8x-5)
(64x^2-40x-40x+25)(8x-5)
(64x^2-80x+25)(8x-5)

(64x^2)(8x)-(80x)(8x)+(25)(8x)+(64x^2)(-5)+
-(80x)(-5)+(25)(-5)
multiply everything and group common

(8x-5)^2 x (8x-5)
(64x^2 -80x +25)(8x-5)
512x^3 -640x^2 +200x -320x^2 +400x -125
512x^3 - 960x^2 + 600x -125

or

pascals triangle
1
11
121
1331
a^3 +3a^2b +3ab^2 +b^3
(8x)^3 + 3(-5)(8x)^2 + 3(8x)(-5)^2 + (-5)^3
512x^3 -960x^2 +600x -125

(8x - 5) (8x - 5)(8x - 5)
(8x - 5) (64x² - 80x + 25)

512 x³ - 640 x² + 200 x
_____- 320 x² + 400 x - 125

512 x³ - 960x² + 600x - 125