nhaanh nhé !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!làm hết

Đáp án+Giải thích các bước giải:

 `16)`

`x^{2}-7xy+12y^{2}`

`=x^{2}-4xy-3xy+12y^{2}`

`=x.(x-4y)-3y.(x-4y)`

`=(x-3y).(x-4y)`

`17)`

`x^{2}-2xy+y^{2}+3x-3y-10`

`=(x^{2}-2.x.y+y^{2})+3.(x-y)-10`

`=(x-y)^{2}+3.(x-y)-10`

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

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

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

`18)`

`2x^{3}-12x^{2}+17x-2`

`=2x^{3}-8x^{2}-4x^{2}+x+16x-2`

`=2x^{2}.(x-2)-8x.(x-2)+1.(x-2)`

`=(x-2).(2x^{2}-8x+1)`

`19)`

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

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

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

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

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

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

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

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

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

`20)`

`x^{3}+3x^{2}+6x+4`

`=x^{3}+2x^{2}+x^{2}+4x+2x+4`

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

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

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

`21)`

`x^{3}+9x^{2}+26x+24`

`=x^{3}+7x^{2}+2x^{2}+12x+14x+24`

`=(x^{3}+7x^{2}+12x)+(2x^{2}+14x+24)`

`=x.(x^{2}+7x+12)+2.(x^{2}+7x+12)`

`=(x+2).(x^{2}+7x+12)`

`=(x+2).(x^{2}+4x+3x+12)`

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

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

`22)`

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

`=2x^{3}-4x^{2}-x^{2}+6x+2x-3`

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

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

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

`23)`

`3x^{3}-14x^{2}+4x+3`

`=3x^{3}-15x^{2}+x^{2}+9x-5x+3`

`=(3x^{3}-15x^{2}+9x)+(x^{2}-5x+3)`

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

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

`24)`

`a^{5}+a+1`

`=a^{5}-a^{4}+a^{4}+a^{3}-a^{3}+a^{2}-a^{2}+a+1`

`=(a^{5}-a^{4}+a^{2})+(a^{4}-a^{3}+a)+(a^{3}-a^{2}+1)`

`=a^{2}.(a^{3}-a^{2}+1)+a.(a^{3}-a^{2}+1)+1.(a^{3}-a^{2}+1)`

`=(a^{3}-a^{2}+1).(a^{2}+a+1).`

`25)`

`a^{7}+a^{2}+1`

`=a^{7}+a^{6}-a^{6}+a^{5}-a^{5}+a^{4}-a^{4}+a^{3}-a^{3}-a^{2}+a^{2}+a^{2}+a-a+1`

`=(a^{7}-a^{6}+a^{4}-a^{3}+a^{2})+(a^{6}-a^{5}+a^{3}-a^{2}+a)+(a^{5}-a^{4}+a^{2}-a+1)`

`=a^{2}.(a^5}-a^{4}+a^{2}-a+1)+a.(a^{5}-a^{4}+a^{2}-a+1)+1.(a^{5}-a^{4}+a^{2}-a+1)`

`=(a^{2}+a+1).(a^{5}-a^{4}+a^{2}-a+1)`

`26)`

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

`=1^{2}+2.1.x^{2}+(x^{2})^{2}-4x+4x^{3}`

`=1+2x^{2}+x^{4}-4x+4x^{3}`

`=x^{4}+2x^{2}+4x^{3}-4x+1`

`=x^{4}+2x^{3}+2x^{3}-x^{2}-x^{2}+4x^{2}-2x-2x+1`

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

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

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

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

`27)`

`x^{4}+6x^{3}+11x^{2}+6x+1`

`=x^{4}+3x^{3}+3x^{3}+9x^{2}+x^{2}+x^{2}+3x+3x+1`

`=(x^{4}+3x^{3}+x^{2})+(3x^{3}+9x^{2}+3x)+1.(x^{2}+3x+1)`

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

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

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