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Đáp án+Giải thích các bước giải:

`5)(x+5).(x^{2}-5x+25)-x.(x-4)^{2}+16x`

`=(x+5).(x^{2}-x.5+5^{2})-x.(x^{2}-2.x.4+4^{2})+16x`

`=x^{3}+5^{3}-x^{3}+8x^{2}-16x+16x`

`=8x^{2}+125`

`7)(x+2).(x^{2}-2x+4)-x.(x-1).(x+1)`

`=(x+2).(x^{2}-x.2+2^{2})-x.(x^{2}-1^{2})`

`=x^{3}+2^{3}-x^{3}+x`

`=x+8`

`9)(x+1).(x^{2}+x+1).(x-1).(x^{2}-x+1)`

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

`=(x^{3}+1^{3]).(x^{3}-1^{3})`

`=(x^{3})^{2}-(1^{3})^{2}`

`=x^{6}-1^{6}`

`=x^{6}-1`

Bài `5:`

 `1)(-x-2)^{3}+(2x-4).(x^{2}+2x+4)-x^{2}.(x-6)`

`=[-(x+2)]^{3}+2.(x-2).(x^{2}+x.2+2^{2])-x^{3}+6x^{2}`

`=-(x^{3}+3.x^{2}.2+3.x.2^{2}+2^{3})+2.(x^{3}-2^{3})-x^{3}+6x^{2}`

`=-x^{3}-6x^{2}-12x-8+2x^{3}-16-x^{3}+6x^{2}`

`=(-x^{3}-x^{3}+2x^{3})+(6x^{2}-6x^{2})-12x-(8+16)`

`=-12x-24`

`2)(x-1)^{3}-(x+2).(x^{2}-2x+4)+3.(x+4).(x-4)`

`=(x^{3]-3.x^{2}.1+3.x.1^{2}-1^{3])-(x+2).(x^{2}-x.2+2^{2})+3.(x^{2}-4^{2})`

`=x^{3}-3x^{2}+3x-1-(x^{3}+2^{3})+3x^{2}-48`

`=x^{3}+3x-1-8-x^{3}-48`

`=3x-57`

`3)(x+y).(x^{2}-xy+y^{2])+3.(2x-y).(4x^{2}+2xy+y^{2})`

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

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

`=x^{3}+3.8x^{3}+y^{3}-3y^{3}`

`=25x^{3}-2y^{3}`

`4)(x+3y).(x^{2}-3xy+9y^{2])+(3x-y).(9x^{2}+3xy+y^{2})`

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

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

`=x^{3}+27x^{3}+27y^{3}-y^{3}`

`=28x^{3}+26y^{3}`