Đáp án:

 Câu `2`

`a, 8x^3 + 36x^2 + 54x + 27`

`= (2x)^3 + 3.(2x)^2 .3 + 3.2x.3^2 +  3^3`

`= (2x + 3)^3`

`b, 27a^2 - 27a^2 + 9a - 1`

`= (3a)^3 - 3.(3a)^2 .1 + 3.3a.1^2 - 1^3`

`= (3a - 1)^3`

`c, (a + 2b)^3 - (a + 2b)(a^2 + 2ab + 4b^2)`

`= a^3 + 3a^2 . 2b + 3.a.(2b)^2 + (2b)^3 - a^3 - 2a^2 b - 4ab^2 - 2a^2 b - 4ab^2 - 8b^3`

`= a^3 + 6a^2 b + 12ab^2 + 8b^3 - a^3 - 2a^2 b - 4ab^2 - 2a^2 b - 4ab^2 - 8b^3`

`= (a^3 - a^3) + (6a^2 b - 2a^2 b - 2a^2 b) + (12ab^2 - 4ab^2 - 4ab^2) + (8b^3 - 8b^3)`

`= 2a^2 b + 4ab^2`

`d, (x - 2y)^3 + 6xy(x - 2y) - x^3`

`= x^3 - 3.x^2 . 2y + 3.x.(2y)^2 - (2y)^3 + 6x^2 y - 12xy^2 - x^3`

`= x^3 - 6x^2 y + 12xy^2 - 8y^3 + 6x^2 y - 12xy^2 - x^3`

`= (x^3 - x^3) + (-6x^2 y + 6x^2 y) + (12xy^2 - 12xy^2) - 8y^3`

`= - 8y^3`

Câu `2`

`a, (x + 2)^3 = x^3 + 3.x^2 . 2 + 3.x.2^2 + 2^3`

`= x^3 + 6x^2 + 12x + 8`

`b, (2x - 3)^3`

`= (2x)^3 - 3.(2x)^2 . 3 + 3.2x.3^2 - 3^3`

`= 8x^3 - 36x^2 + 54x - 27`

`c, ((2x)/3 + (3y)/2)^3`

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

`= (8x^3)/27 + 2x^2 y + 9/2 xy^2 + (27y^3)/8`

`d, (2x^2 y - xy)^3`

`= (2x^2 y)^3 - 3.(2x^2 y)^2 . xy + 3.2x^2 y . (xy)^2 - (xy)^3`

`= 8x^6 y^3 - 12x^5 y^3 + 6x^4 y^3 - x^3 y^3`

`e, 27x^3 + 8y^3`

`= (3x)^3 + (2y)^3`

`= (3x + 2y)[(3x)^2 - 3x.2y + (2y)^2]`

`= (3x + 2y)(9x^2 - 6xy + 4y^2)`

`f, (x^3 y^6)/8 - 27/y^3`

`= ((xy^2)/2)^3 - (3/y)^3`

`= ((xy^2)/2 - 3/y)[((xy^2)/2)^2 + (xy^2)/2 . 3/y + (3/y)^2]`

`= ((xy^2)/2 - 3/y)((x^2 y^4)/4 + (3xy^2)/(2y) + 9/(y^2))`