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)-

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

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

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

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

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

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

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

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

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