Đáp án+Giải thích các bước giải:

 bài `4:`

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

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

`=1.(x^{2}+2x+1+x^{2}+x+x^{2})-x^{2}+16`

`=3x^{2}+3x+1-x^{2}+16`

`=2x^{2}+3x+17`

`2)(x+2)^{3}-x.(x+3).(x-3)-12x^{2}-8`

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

`=x^{3}+6x^{2}-12x^{2}+12x+8-8-x^{3}+9x`

`=-6x^{2}+21x`

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

`=(x-2).[(x-2)^{2}-x.(x+2)]+6x^{2}-18x`

`=(x-2).(x^{2}-2.x.2+2^{2}-x^{2}-2x)+6x^{2}-18x`

`=(x-2).(-6x+4)+6x^{2}-18x`

`=-6x^{2}+4x+12x-8+6x^{2}-18x`

`=-2x-8`

`4)x.(x-5).(x+5)-(x-5)^{3}+100x`

`=(x-5).[x.(x+5)-(x-5)^{2}]+100x`

`=(x-5).[x^{2}+5x-(x^{2}-2.x.5+5^{2})]+100x`

`=(x-5).(x^{2}+5x-x^{2}+10x-25)+100x`

`=(x-5).(15x-25)+100x`

`=15x^{2}-25x-75x+100x+125`

`=15x^{2}+125`