Đáp án:
`1)(x^2-9)+12x(x-3)^2=(x-3)(12x^2-35x+3).`
`2)24ab(a^2 -b^2)-6(a^3+a^2b-b^3)+9(a^2-b^2=3(8a^3b-8ab^3-2a^3-2a^2b+2b^3+3a^2-3b^2).`
`3)x^3(x^2+1)^2-9x=x(x^3+x+3)(x^2+x-3).`
`4)x^6y-x^4y^3-x^3y^4+xy^6=xy(x+y)(x-y)^2(x^2+xy+y^2).`
`5)x^3y^3z^3+x^2y^2z^2-xyz-1=(xyz+1)^2(xyz-1).`
Giải thích các bước giải.
`1)(x^2-9)+12x(x-3)^2`
`=(x-3)(x+3)+12x(x-3)(x-3)`
`=(x-3)[(x+3)+12x(x-3)]`
`=(x-3)(12x^2-35x+3).`
`2)24ab(a^2 -b^2)-6(a^3+a^2b-b^3)+9(a^2-b^2)`
`=3[8ab(a^2 -b^2)-2(a^3+a^2b-b^3)+3(a^2-b^2)]`
`=3(8a^3b-8ab^3-2a^3-2a^2b+2b^3+3a^2-3b^2).`
`3)x^3(x^2+1)^2-9x`
`=x[x^2(x^2+1)^2-9]`
`=x{[x(x^2+x)]^2-3^2}`
`=x[(x^3+x)^3-3^2]`
`=x(x^3+x+3)(x^2+x-3).`
`4)x^6y-x^4y^3-x^3y^4+xy^6`
`=(x^6y+xy^6)-(x^4y^3+x^3y^4)`
`=xy(x^5+y^5)-x^3y^3(x+y)`
`=xy[x^5+y^5-x^2y^2(x+y)]`
`=xy(x^5+y^5-x^3y^2-x^2y^3)`
`=xy[(x^5-x^3y^2)+(y^5-x^2y^3)]`
`=xy[x^3(x^2-y^2)+y^3(y^2-x^2)]`
`=xy(x^2-y^2)(x^3-y^3)`
`=xy(x+y)(x-y)(x-y)(x^2+xy+y^2)`
`=xy(x+y)(x-y)^2(x^2+xy+y^2).`
`5)x^3y^3z^3+x^2y^2z^2-xyz-1`
`=(x^3y^3z^3+x^2y^2z^2)-(xyz+1)`
`=x^2y^2(xyz+1)-(xyz+1)`
`=(xyz+1)(x^2y^2z^2-1)`
`=(xyz+1)(xyz+1)(xyz-1)`
`=(xyz+1)^2(xyz-1).`
