Đáp án:
a/ $(y+3)(xy-5)$
b/ $(x-y-3)(x+y-3)$
c/ $(2x-2y+1)(2x+2y+1)$
d/ $(x-y)(x^2+xy+y^2+1)$
e/ $(x-y)(x+z)(y+z)$
Giải thích các bước giải:
a/ $xy^2+3xy-5y-15$
$=xy(y+3)-5(y+3)$
$=(y+3)(xy-5)$
b/ $x^2-6x-y^2+9$
$=(x^2-6x+9)-y^2$
$=(x-3)^2-y^2$
$=(x-y-3)(x+y-3)$
c/ $4x^2-4y^2+4x+1$
$=(4x^2+4x+1)-4y^2$
$=(2x+1)^2-(2y)^2$
$=(2x-2y+1)(2x+2y+1)$
d/ $x^3+x-y^3-y$
$=(x^3-y^3)+(x-y)$
$=(x-y)(x^2+xy+y^2)+(x-y)$
$=(x-y)(x^2+xy+y^2+1)$
e/ $x^2(y-z)+y^2(z-x)+z^2(x-y)$
$=z^2(x-y)+x^2y-x^2z-xy^2+y^2z$
$=z^2(x-y)+(x^2y-xy^2)-(x^2z-y^2z)$
$=z^2(x-y)+xy(x-y)+z(x^2-y^2)$
$=z^2(x-y)+xy(x-y)+z(x+y)(x-y)$
$=(x-y)(z^2+xy+xz+yz)$
$=(x-y)[(z^2+xz)+(xy+yz)]$
$=(x-y)(x+z)(y+z)$
