Đáp án + Giải thích các bước giải:
CT: `(A±B)^2=A^2±2AB+B^2`
`A^2-B^2=(A-B)(A+B)`
`19) x^3+x^2y-xy^2-y^3=x^2(x+y)-y^2(x+y)`
`=(x+y)(x^2-y^2)=(x+y)(x-y)(x+y)=(x+y)^2(x-y)`
`20)x^2y^2+1-x^2-y^2=x^2y^2-x^2-y^2+1`
`=x^2(y^2-1)-(y^2-1)=(y^2-1)(x^2-1)`
`=(y-1)(y+1)(x-1)(x+1)`
`21)4x^2y^2-(x^2+y^2-1)^2=(2xy)^2-(x^2+y^2-1)^2`
`=(2xy-x^2-y^2+1)(2xy+x^2+y^2-1)`
`=(-x^2+2xy-y^2+1)(x^2+2xy+y^2-1)`
`=-(x^2-2xy+y^2-1)(x^2+2xy+y^2-1)`
`=-[(x-y)^2-1][(x+y)^2-1]`
`=-(x-y-1)(x-y+1)(x+y-1)(x+y+1)`
`22)(xy+4)^2-(2x+2y)^2=(xy+4-2x-2y)(xy+4+2x+2y)`
`23)x^2-y^2-4x+4y=(x-y)(x+y)-4(x-y)`
`=(x-y)(x+y-4)`
`24)3x-3y+x^2-2xy+y^2=3(x-y)+(x-y)^2`
`=(x-y)(3+x-y)`
