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Đáp án: $13)(x+y)(x-y-1)$

             $14)(x-y-z)(x-y+z)$

             $15)(a^2-y)(a-x)$

             $16)(x-y-2z)(x-y+2z)$

             $17)(2x+1-y)(2x+1+y)$

             $18)(x+y)(x^2-xy+y^2-1)$

             $19)x^2(x+1)^2$

             $20)5(x-y-2z)(x-y+2z)$

             $21)(x+y)(x+y-1)(x+y+1)$

Giải thích các bước giải:

$13)x^2-x-y^2-y$

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

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

$=(x+y)(x-y-1)$

$14)x^2-2xy+y^2-z^2$

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

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

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

$15)a^3-a^2x-ay+xy$

$=(a^3-a^2x)-(ay-xy)$

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

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

$16)x^2-2xy-4z^2+y^2$

$=(x^2-2xy+y^2)-4z^2$

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

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

$17)4x^2-y^2+4x+1$

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

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

$=(2x+1-y)(2x+1+y)$

$18)x^3-x+y^3-y$

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

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

$=(x+y)(x^2-xy+y^2-1)$

$19)x^4+2x^3+x^2$

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

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

$20)5x^2-10xy+5y^2-20z^2$

$=5(x^2-2xy+y^2-4z^2)$

$=5[(x^2-2xy+y^2)-4z^2]$

$=5[(x-y)^2-(2z)^2]$

$=5(x-y-2z)(x-y+2z)$

$21)x^3-x+3x^2y+3xy^2+y^3-y$

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

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

$=(x+y)[(x+y)^2-1]$

$=(x+y)(x+y-1)(x+y+1)$