`a)(x+3)(x^2+3x+9)-(54+x^3)`

`=x^3+3x^2+9x+3x^2+9x+27-54-x^3`

`=(x^3-x^3)+(3x^2+3x^2)+(9x+9x)+(27-54)`

`=6x^2+18x-27`

Sửa đề:`(x+3)(x^2+3x+9)-(54+x^3)`

`→(x+3)(x^2-3x+9)-(54+x^3)`

`(x+3)(x^2-3x+9)-(54+x^3)`

`=(x+3)(x^2-x.3+3^2)-54-x^3`

`=x^3+3^3-54-x^3`

`=x^3+27-54-x^3`

`=(x^3-x^3)+(27-54)`

`=-27`

`b)(2x+y)(4x²-2y+y²)-(2x-y)(4x²+2xy+y²)`

`=8x³-4xy+2xy²+4x²y-2y²+y³-(2x-y)[(2x)²+2x.y+y²]`

`=8x³-4xy+2xy²+4x²y-2y²+y³-[(2x)³-y³]`

`=8x³-4xy+2xy²+4x²y-2y²+y³-(8x³-y³)`

`=8x³-4xy+2xy²+4x²y-2y²+y³-8x³+y³`

`=(8x³-8x³)-4xy+2xy²+4x²y-2y²+(y³+y³)`

`=-4xy+2xy²+4x²y-2y²+2y³`

Sửa đề:`(2x+y)(4x²-2y+y²)-(2x-y)(4x²+2xy+y²)`

`→(2x+y)(4x²-2xy+y²)-(2x-y)(4x²+2xy+y²)`

`(2x+y)(4x²-2xy+y²)-(2x-y)(4x²+2xy+y²)`

`=(2x+y)[(2x)²-2x.y+y²]-(2x-y)[(2x)²+2x.y+y²]`

`=(2x)³+y³-[(2x)³-y³]`

`=8x³+y³-(8x³-y³)`

`=8x³+y³-8x³+y³`

`=(8x³-8x³)+(y³+y³)`

`=2y³`

`a)`

`(x+3)(x^2- 3x+9) - (54+x^3)`

`=  (x+3)(x^2 - x . 3 + 3^2) - (54 + x^3)`

`=  (x^3 + 3^3) - (54 + x^3)`

` = (x^3 + 27) - (54 +x^3)`

`= x^3 + 27 - 54-  x^3`

`=  (x^3 - x^3) + (27-54)`

`=  -27`

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`(x+3)(x^2 + 3x+9) - (54 + x^3)`

`=  (x^3 + 3x^2 + 9x + 3x^2 + 9x + 27) - (54+x^3)`

`=  x^3 + 3x^2 + 9x + 3x^2 + 9x + 27 - 54 - x^3`

` = (x^3 - x^3) + (3x^2 + 3x^2) + (9x+9x) + (27-54)`

`=  6x^2 + 18x -27`

`b)`

`(2x+y)(4x^2 - 2xy + y^2) - (2x-y)(4x^2 + 2xy + y^2)`

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

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

`=  (8x^3 + y^3) - (8x^3 -y^3)`

`=  8x^3 + y^3 - 8x^3 + y^3`

` = (8x^3-8x^3) + (y^3+y^3)`

` = 2y^3`

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`(2x+y)(4x^2 - 2y + y^2) - (2x-y)(4x^2 + 2xy + y^2)`

` = (8x^3 - 4xy + 2xy^2 + 4x^2y - 2y^2 + y^3) - (2x-y) [ (2x)^2 + 2x . y + y^2]`

`=  (8x^3 - 4xy + 2xy^2 + 4x^2y - 2y^2 + y^3) - [ (2x)^3 - y^3]`

`=  (8x^3 - 4xy + 2xy^2 + 4x^2y - 2y^2 + y^3) - (8x^3 - y^3)`

`=  8x^3 - 4xy + 2xy^2 + 4x^2y - 2y^2 + y^3-  8x^3 + y^3`

`=  (8x^3 - 8x^3) + (y^3 + y^3) - 4xy + 2xy^2 + 4x^2y - 2y^2`

`=  2y^3 - 4xy + 2xy^2 + 4x^2y - 2y^2`