Question

a, (x+2)^3 b, (x+1)^3 c, (2x-1)^3 d, (xy+3)^3 e, (2x+3y)^3 f, (3x-y)^3 g, (1/3x-2)^3 

h,(x^2+1/2y)^3

Answer 1

`(x+2)^3 = x^3 + 3x^2 . 2 + 3x . 2^2 + 2^3 = x^3 + 6x^2 + 12x + 8`

`(x+1)^3 = x^3 + 3x^2 . 1 + 3x.1^2 + 1^3 = x^3 + 3x^3 + 3x + 1`

`(2x - 1)^3 = (2x)^3 - 3.(2x)^2 . 1 + 3.2x . 1^2 - 1^3 = 8x^3 - 12x^2 + 6x - 1`

`(xy+3)^3 = (xy)^3 + 3.(xy)^2 . 3 + 3xy.3^2 + 3^3 = x^3 y^3 + 9x^2 y^2 + 27xy + 27`

Answer 2

`(3x - y)^3 = (3x)^3 - 3.(3x)^2 . y + 3.3x . y^2 - y^3 = 27x^3 - 27x^2 y + 9xy^2 - y^3`

`(1/3 x - 2)^3 = (1/3x)^3 - 3 .(1/3x)^2 .2 + 3 . (1/3x) . 2^2 - 2^3 = 1/27 x^3 - 2/3 x^2 + 4x - 8`

`(x^2 + 1/2y)^3 = (x^2)^3 + 3 . (x^2)^2 . 1/2y + 3 . x^2 . (1/2y)^2 + (1/2y)^3 `

`= x^6 + 3/2 x^4 y + 3/4 x^2 y^2 + 1/8 y^3`