因式分解高端题目汇总.doc

1.(2x+3y)+(3x+2y)-125(x-y)解法：原式=(2x-3y)+(3x-2y)-5(x-y) =(2x-3y)+(3x-2y)-(2x-3y)+(3x-2y) = -15x(x-y)(2x-3y)(3x-2y)2.(x+5x+2)(x+5x+3)-12解法：设x+5x=a,则 原式=(a+2)(a+3)-12 =a+5a-6 =(a+6)(a-1) =(x+5x+6)(x+5x-1) =(x+2)(x+3)(x+5x-1)3.(x+1)(x+2)(x+3)(x+6)+x解法：原式=(x+7x+6)(x+5x+6) =(x+6x+6) 提示：令x+6x=a4.(x+y)(x+y+xy)+(xy+1)(xy-1)解法：令x+y=a,xy=b,则 原式=a(a+2b)+(b+1)(b-1) =a+2ab+b-1 =(a+b)-1 =(a+b+1)(a+b-1） =(x+y+xy+1)(x+y+xy-1) =(x+1)(y+1)(xy+x+y-1)5.a-ab+ac-2bc解法：原式=(a-ab)+(ac-bc) =a(a-b)+c(a-b) =(a+c)(a-b)6.x-4y-z+4yz解法：原式=x-(4y+z-4yz) =x-(2y-z) =(x-2y+z)(x+2y-z)7.x+6x+11x+6解法：原式=(x+x)+(5x+5x)+(6x+6) =x(x+1)+5x(x+1)+6(x+1) =(x+1)(x+5x+6) =(x+1)(x+2)(x+3)8.x4+2x-9x+8解法：原式=(x4+2x)-(x+2x)-(8x-8) =x(x+2)-x(x+2)-8(x+1)(x-1) =(x+2)(x-x)-8(x+1)(x-1) =x(x+2)(x-1)-8(x+1)(x-1) =x(x+2)(x+1)(x-1)-8(x+1)(x-1) =(x+1)(x-1)(x+2x-8) =(x+1)(x-1)(x-2)(x+4)9.4a-b+6a-3b解法：原式=(2a+b)(2a-b)+3(2a+b) =(2a-b)(2a+b+3)10.9a-4b+4bc-c解法：原式=9a-(4b-4bc+c) =9a-(2b-c) =(3a+2b-c)(3a-2b+c)11.(a+c)(a-c)+b(b-2a)解法：原式=a-c+b-2bc =(a-2ab+b)-c =(a-b)-c =(a-b-c)(a-b+c)12.(x+x+1)(x+x+2)-12解法：设x+x=a,则 原式=(a+1)(a+2)-12 =a+3a-10 =(a-2)(a+5) =(x+x-2)(x+x+5) =(x-1)(x+2)(x+x+5)13.(2x-3x+1)-22x+33x-1解法：原式=(2x-3x+1)-11(2x-3x)-1此时，设2x-3x=a,则 =(a+1)-11a-1 =a+2a+1-11a-1 =a-9a =a(a-9) =(2x-3)(2x-3-9) =x(2x-3)(x-3)(2x+3)14.(x-1)(x+3)(x+5)+12解法：原式=(x+1)(x-1)(x+3)(x+5)此时，将(x+1)和(x+3)相乘，将(x-1)和(x+5)相乘。得： (x+4x+3)(x+4x