因式分解高端题目汇总

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1、1.(2x+3y)³+(3x+2y)³-125(x-y)³解法：原式=(2x-3y)³+(3x-2y)³-[5(x-y)]³                   =(2x-3y)³+(3x-2y)³-[(2x-3y)+(3x-2y)]³                   =-15x(x-y)(2x-3y)(3x-2y)2.(x²+5x+2)(x²+5x+3)-12解法：设x²+5x=a,则           原式=(a+2)(a+3)-12                    =a²+5a-6      

2、             =(a+6)(a-1)                   =(x²+5x+6)(x²+5x-1)                   =(x+2)(x+3)(x²+5x-1)3.(x+1)(x+2)(x+3)(x+6)+x²解法：原式=(x²+7x+6)(x²+5x+6)                   =(x²+6x+6)²                           提示：令x²+6x=a4.(x+y)(x+y+xy)+(xy+1)(xy-1)解法：令x+y=a,xy

3、=b,则           原式=a(a+2b)+(b+1)(b-1)                   =a²+2ab+b²-1                   =(a+b)²-1                   =(a+b+1)(a+b-1）                   =(x+y+xy+1)(x+y+xy-1)                   =(x+1)(y+1)(xy+x+y-1)5.a²-ab+ac-2bc解法：原式=(a²-ab)+(ac-bc)              

4、      =a(a-b)+c(a-b)                   =(a+c)(a-b)6.x²-4y²-z²+4yz解法：原式=x²-(4y²+z²-4yz)                   =x²-(2y-z)²                   =(x-2y+z)(x+2y-z)7.x³+6x²+11x+6解法：原式=(x³+x²)+(5x²+5x)+(6x+6)                 =x²(x+1)+5x(x+1)+6(x+1)                 =(x+1)

5、(x²+5x+6)                =(x+1)(x+2)(x+3)8.x^4+2x³-9x²+8解法：原式=(x^4+2x³)-(x²+2x)-(8x²-8)                 =x³(x+2)-x(x+2)-8(x+1)(x-1)                =(x+2)(x³-x)-8(x+1)(x-1)                =x(x+2)(x²-1)-8(x+1)(x-1)                =x(x+2)(x+1)(x-1)-8(x+1)(x-1) 

6、               =(x+1)(x-1)(x²+2x-8)                =(x+1)(x-1)(x-2)(x+4)9.4a²-b²+6a-3b解法：原式=(2a+b)(2a-b)+3(2a+b)                   =(2a-b)(2a+b+3)10.9a²-4b²+4bc-c²解法：原式=9a²-(4b²-4bc+c²)                    =9a²-(2b-c)²                   =(3a+2b-c)(3a-2b+c)11.

7、(a+c)(a-c)+b(b-2a)解法：原式=a²-c²+b²-2bc                   =(a²-2ab+b²)-c²                   =(a-b)²-c²                   =(a-b-c)(a-b+c)12.(x²+x+1)(x²+x+2)-12解法：设x²+x=a,则           原式=(a+1)(a+2)-12                     =a²+3a-10                    =(a-2)(a+5)   

8、                 =(x²+x-2)(x²+x+5)                    =(x-1)(x+2)(x²+x+5)13.(2x²-3x+1)²-22x²+33x-1解法：原式=(2x²-3x+1)²-11(2x²-3x)-1此时，设2x²-3x=a,则                   =(a+1)²-11a-1                   =