Đáp án+Giải thích các bước giải:
`1) x^2 -xy +y^2 -z^2 ->` Sai đề
`2) xy - 3x -y^2 +3y`
`=(xy-y^2)-(3x-3y)`
`=y(x-y)-3(x-y)`
`=(y-3)(x-y)`
`3) x^2 -9 +(x-3)^2`
`=(x-3)(x+3)+(x-3)^2`
`=(x-3)(x+3+x-3)`
`=2x(x-3)`
`4) x^2 -2xy +x-2y`
`= (x^2+x)-(2xy +2y)`
`=x(x+1)-2y(x+1)`
`=(x-2y)(x+1)`
`5) x^2 +xy -xz - yz`
`=(x^2+ xy)-(xz+yz)`
`=x(x+y)-z(x+y)`
`=(x-z)(x+y)`
`6) x^2-6x-y^2 +9`
`=(x^2 -6x+9)-y^2`
`=(x-3)^2 - y^2`
`=(x-3-y)(x-3+y)`
`7) x^3 - 2x^2 +x - xy^2`
`=x(x^2 -2x +1-y^2)`
`=x [(x-1)^2-y^2]`
`=x(x-1-y)(x-1+y)`
`8) x^2 -2x +2y -xy`
`=(x^2 -2x)-(xy-2y)`
`=x(x-2)-y(x-2)`
`=(x-y)(x-2)`
`9) 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)`
`10) xy^2 -x^3 +2x^2 -x`
`=x(y^2 -x^2 +2x -1)`
`=x[y^2 - (x^2 - 2x+1)]`
`=x[y^2 - (x-1)^2]`
`=x(y-x+1)(y+x-1)`
`11) x^2 +xy -2x - 2y`
`=x(x+y)-2(x+y)`
`=(x-2)(x+y)`
`12) x^2(x^2-6)-x^2+9`
`= x^4 - 6x^2 -x^2 +9`
`=(x^4 - 6x^2 +9)-x^2`
`=(x^2 -3)^2 - x^2`
`=(x^2-3-x)(x^2-3+x)`
`13) y^2 - 3xy +6y -18x`
`=(y^2+6y)-(3xy+18x)`
`= y(y+6) - 3x(y+6)`
`=(y-3x)(y+6)`
`14) 3x(x-y)+6(y-x)`
`=3x(x-y)-6(x-y)`
`=(3x-6)(x-y)`
`=3(x-2)(x-y)`
`15) 9(x-2)^2 - (y+3)^2`
`= 3^2 (x-2)^2 - (y+3)^2`
`= (3x-6)^2 - (y+3)^2`
`=(3x-6-y-3)(3x-6+y+3)`
`= (3x-y-9)(3x+y-3)`
`16) x^6 - x^4 - 9x^3 +9x^2`
`=(x^6 - x^4)-(9x^3-9x^2)`
`=x^4(x^2-1)-9x^2(x-1)`
`=x^4(x-1)(x+1)-9x^2(x-1)`
`=(x-1)(x^5 +x^4 -9x^2)`
`=x^2(x-1)(x^3+x^2-9)`
`17) x(y^2-1)+4(1-y^2)`
`=x(y^2-1)-4(y^2-1)`
`=(x-4)(y^2-1)`
`=(x-2)(y-1)(y+1)`
`18) x^2 - 4y^2 +16x +64`
`=(x^2 +16x + 64)-4y^2`
`=(x+8)^2-(2y)^2`
`=(x+8+2y)(x+8-2y)`
`19) xy^2+2y^2 +2xy +4y`
`=(xy^2+2y^2)+(2xy+4y)`
`=y^2(x+2)+2y(x+2)`
`=(y^2+2y)(x+2)`
`=y(y+2)(x+2)`
`20) 10x(x-y)-6y(y-x)`
`=10x(x-y)+6y(x-y)`
`=(10x+6y)(x-y)`
`=2(5x + 3y)(x-y)`
`21) 25(x+5)^2 - 9(x+7)^2`
`=5^2 (x+5)^2 - 3^2 (x+7)^2`
`=(5x + 25)^2 -(3x + 21)^2`
`=(5x+25 - 3x - 21)(5x+25+3x+21)`
`=(2x + 4)(8x+46)`
`=4(x+2)(4x + 23)`
