Đáp án `+` Giải thích các bước giải:

`i)` `3x(9-x)^2-(x-9)^2`

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

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

`k)` `10x(x-y)-8x^2(y-x)`

`= 10x(x-y)+8x^2(x-y)`

`= (10x+8x^2)(x-y)`

`= 2x(5+4x)(x-y)`

`l)` `4x(x-2y)+8y(2y-x)`

`= 4x(x-2y)-8y(x-2y)`

`= (4x-8y)(x-2y)`

`= 4(x-2y)(x-2y)`

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

`m)` `x^2-z^2-2xy+y^2`

`= (x^2-2xy+y^2)-z^2`

`= (x-y)^2-z^2`

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

`n)` `x(x+1)^2+x(x-5)-5(x+1)^2`

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

`= (x-5)[(x+1)^2+x]`

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

`= (x-5)(x^2+3x+1)`

`o)` `x^3+x^2+x+1`

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

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

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

`ô)`

`2x^2+4x+2-2y^2`

`= 2(x^2+2x+1-y^2)`

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

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

`= 2(x-y+1)(x+y+1)`

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

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

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

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`10x (x-y) - 8x^2 (y-x)`

` = 10x (x-y) + 8x^2 (x-y)`

` = (10x + 8x^2) (x-y)`

` = 2x (5 + 4x) (x-y)`

---

`4x (x-2y) + 8y (2y - x)`

` = 4x (x-2y) - 8y (x - 2y)`

` = (4x-8y)(x-2y)`

` = 4 (x-2y)(x-2y)`

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

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`x^2 - z^2 - 2xy + y^2`

` = (x^2-2xy+y^2) -z^2`

`=  (x-y)^2 - z^2`

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

---

`x (x+1)^2 + x (x-5) - 5 (x+1)^2`

`= [ x (x+1)^2 - 5 (x+1)^2] + x (x-5)`

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

`=  (x-5) [(x+1)^2+x]`

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

` = (x-5)(x^2+3x+1)`

---

`x^3 + x^2 + x + 1`

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

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

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`2x^2 + 4x + 2 - 2y^2`

` = 2 (x^2 + 2x + 1 - y^2)`

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

` = 2 (x+1+y)(x+1-y)`