a) xy ² + 3xy -5y-15 b)x ² -6x -y ² +9 c) 4x ² -4y ² +4x + 9 d)x ³ +x -y ³ -y e)x ²(y-x)+y ²(z-x)+z ²(x-y)-

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/ $x^2(y-z)+y^2(z-x)+z^2(x-y)$

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

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

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

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

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

$=(x-y)[(z^2+xz)+(xy+yz)]$

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