Đáp án:

Giải thích các bước giải:

 bài 1:

$a)6x^2.(3x^2-4x+5)$

$=18x^4-24x^3+30x^2$

$b)(x-2y).(3xy+6y^2+x)$

$=3x^2y+6xy^2+x^2-6xy^2-12y^3-2xy$

$=-12y^3+3x^2y+x^2-2xy$

$c)(18x^4y^3-24x^3y^4+12x^3y^3):(-6x^2y^3)$

$=-3x^2+4xy-2x$

bài 2:

$a)3x^2-3xy-5x+5y$

$=3x.(x-y)-5.(x-y)$

$=(x-y).(3x-5)$

$b)x^2+4x-45$

$=x^2+4x+4-49$

$=(x+2)^2-7^2$

$=(x+2-7).(x+2+7)$

$=(x-5).(x+9)$

$c)3y^3+6xy^2+3x^2y$

$=3y.(y^2+2xy+x^2)$

$=3y.(x+y)^2$

$d)x^3-3x^2-4x+12$

$=(x^3-3x^2)-(4x-12)$

$=x^2.(x-3)-4.(x-3)$

$=(x-3).(x^2-4)$

$=(x-3).(x-2).(x+2)$

$e)x^3+3x^2-3x-1$

$=(x^3-1)+(3x^2-3x)$

$=(x-1).(x^2+x+1)+3x.(x-1)$

$=(x-1).(x^2+x+1+3x)$

$=(x-1).(x^2+4x+1)$

$f)x^2-3x+xy-3y$

$=(x^2+xy)-(3x+3y)$

$=x.(x+y)-3.(x+y)$

$=(x+y).(x-3)$

$g)x^2-2xy+y^2-4$

$=(x-y)^2-2^2$

$=(x-y-2).(x-y+2)$

$h)x^2-2xy+y^2-z^2$

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

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

$=(x-y-z).(x-y+z)$

$i)3x^2+6xy+3y^2-3z^2$

$=3.[ x^2+2xy+y^2-z^2]$

$=3.[ (x^2+2xy+y^2)-z^2]$

$=3.[ (x+y)^2-z^2]$

$=3.(x+y-z).(x+y+z)$

Đáp án:

Giải thích các bước giải:

`a)6x^2.(3x^2-4x+5)`

`=18x^4-24x^3+30x^2`

`b)(x-2y).(3xy+6y^2+x)`

`=3x^2y+6xy^2+x^2-6xy^2-12y^3-2xy`

`=-12y^3+3x^2y+x^2-2xy`

`c)(18x^4y^3-24x^3y^4+12x^3y^3):(-6x^2y^3)`

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

bài 2:

`a)3x^2-3xy-5x+5y`

`=3x.(x-y)-5.(x-y)`

`=(x-y).(3x-5)`

`b)x^2+4x-45`

`=x^2+4x+4-49`

`=(x+2)^2-7^2`

`=(x+2-7).(x+2+7)`

`=(x-5).(x+9)`

$c)3y^3+6xy^2+3x^2y$

$=3y.(y^2+2xy+x^2)$

$=3y.(x+y)^2$

$d)x^3-3x^2-4x+12$

$=(x^3-3x^2)-(4x-12)$

$=x^2.(x-3)-4.(x-3)$

$=(x-3).(x^2-4)$

$=(x-3).(x-2).(x+2)$

$e)x^3+3x^2-3x-1$

$=(x^3-1)+(3x^2-3x)$

$=(x-1).(x^2+x+1)+3x.(x-1)$

$=(x-1).(x^2+x+1+3x)$

$=(x-1).(x^2+4x+1)$

$f)x^2-3x+xy-3y$

$=(x^2+xy)-(3x+3y)$

$=x.(x+y)-3.(x+y)$

$=(x+y).(x-3)$

$g)x^2-2xy+y^2-4$

$=(x-y)^2-2^2$

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

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

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

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

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

`i)3x^2+6xy+3y^2-3z^2`

`=3.[ x^2+2xy+y^2-z^2]`

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

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

`=3.(x+y-z).(x+y+z)`