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:
$13)x^2-x-y^2-y$
$=(x^2-y^2)-(x+y)$
$=(x-y)(x+y)-(x+y)$
$=(x+y)(x-y-1)$
$14)x^2-2xy+y^2-z^2$
$=(x^2-2xy+y^2)-z^2$
$=(x-y)^2-z^2$
$=(x-y-z)(x-y+z)$
$15)a^3-a^2x-ay+xy$
$=(a^3-a^2x)-(ay-xy)$
$=a^2(a-x)-y(a-x)$
$=(a^2-y)(a-x)$
$16)x^2-2xy-4z^2+y^2$
$=(x^2-2xy+y^2)-4z^2$
$=(x-y)^2-(2z)^2$
$=(x-y-2z)(x-y+2z)$
$17)4x^2-y^2+4x+1$
$=(4x^2+4x+1)-y^2$
$=(2x+1)^2-y^2$
$=(2x+1-y)(2x+1+y)$
$18)x^3-x+y^3-y$
$=(x^3+y^3)-(x+y)$
$=(x+y)(x^2-xy+y^2)-(x+y)$
$=(x+y)(x^2-xy+y^2-1)$
$19)x^4+2x^3+x^2$
$=x^2(x^2+2x+1)$
$=x^2(x+1)^2$
$20)5x^2-10xy+5y^2-20z^2$
$=5(x^2-2xy+y^2-4z^2)$
$=5[(x^2-2xy+y^2)-4z^2]$
$=5[(x-y)^2-(2z)^2]$
$=5(x-y-2z)(x-y+2z)$
$21)x^3-x+3x^2y+3xy^2+y^3-y$
$=(x^3+3x^2y+3xy^2+y^3)-(x+y)$
$=(x+y)^3-(x+y)$
$=(x+y)[(x+y)^2-1]$
$=(x+y)(x+y-1)(x+y+1)$
