phân tích đa thức thành nhân tử a) x²-y²-2x+2y b) 2x+2y-x²-xy c) 3a²-6ab+3b²-12c² d) x²-25+y²+2xy e) a²+2ab+b²-ac-bc

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1. a) $x^2-y^2-2x+2y$

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

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

   b) $2x+2y-x^2-xy$

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

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

   c) $3a^2-6ab+3b^2-12c^2$

   $=3.(a^2-2ab+b^2)-4c^2$

   $=3.[(a-b)^2-(2c)^2]$

   $=3.(a-b-2c).(a-b+2c)$

   d) $x^2-25+y^2+2xy$

   $=(x^2+2xy+y^2)-25$

   $=(x+y)^2-25$

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

   e) $a^2+2ab+b^2-ac-bc$

   $=(a^2+2ab+b^2)-c.(a+b)$

   $=(a+b)^2-c.(a+b)$

   $=(a+b)(a+b-c)$

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2. $a) x²-y²-2x+2y$

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

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

   $b) 2x+2y-x²-xy$

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

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

   $c) 3a²-6ab+3b²-12c²$

   $= 3(a²-2ab+b²-4c²)$

   $= 3[(a-b)²-(2c)²]$

   $= 3(a-b+2c)(a-b-2c)$

   $d) x²-25+y²+2xy$

   $= x²+2xy+y²-25$

   $= (x+y)²-5²$

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

   $e) a²+2ab+b²-ac-bc$

   $= (a+b)²-c(a+b)$

   $= (a+b)(a+b-c)$

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