Bài `1:`

`a) (x+2y)^2`

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

`=x^2 + 4xy + 4y^2`

`b) (x-1/2)^2`

`=x^2 - 2 . x . 1/2 + (1/2)^2`

`=x^2 - x + 1/4`

`c) (5x-2y)^2`

`=(5x)^2 - 2 . 5x . 2y + (2y)^2`

`=25x^2 - 20x + 4y^2`

`d) 4x^2 - 9`

`=(2x)^2-3^2`

`=(2x-3)(2x+3)`

`e) 25x^2 - 1/4`

`=(5x)^2 - (1/2)^2`

`=(5x-1/2)(5x+1/2)`

`f) (x-y)^2 - (x+y)^2`

`=[(x-y) + (x+y)] . [(x-y)-(x+y)]`

`=(x-y+x+y)(x-y-x-y)`

`=2x . (-2y)`

`=-4xy`

`g) (3x+4y)^3`

`=(3x)^3 + 3 . (3x)^2 . 4y + 3 . 3x . (4y)^2 + (4y)^3`

`=27x^3 + 12y . 9x^2 + 9x . 16y^2 + 64y^3`

`=27x^3 + 108x^2y + 144xy^2 + 64y^3`

`h) (x-3y)^3`

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

`=x^3 - 9x^2y + 27xy^2 - 27y^3`

`i) (x - 2/5)^3`

`=x^3 - 3 . x^2 . 2/5 + 3 . x . (2/5)^2 - (2/5)^3`

`=x^3 - 6/5 x^2 + 12/25 x - 8/125`

`k) x^3 +8`

`=x^3 + 2^3`

`=(x+2)(x^2 - 2x + 4)`

`l) x^3-64`

`=x^3 - 4^3`

`=(x-4)(x^2 + 4x + 16)`

`m) 27x^3+1`

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

`=(3x+1)[(3x)^2 - 3x . 1 + 1^2]`

`=(3x+1)(9x^2 -3x+1)`

`o) 64x^3 - 27`

`=(4x)^3 - 3^3`

`=(4x-3)[(4x)^2 + 4x . 3 + 3^2]`

`=(4x-3)(16x^2 + 12x+9)`