1.4(x+5)(x+6)(x+10)(x+12)-3x·x

1。4(x+5)(x+6)(x+10)(x+12)－3x^2= 4*[(x+5)(x+12)][(x+6)(x+10)] - 3x^2= 4*(x^2 + 60 + 17x)(x^2 + 60 + 16x) - 3x^2= 4*[(x^2+60)^2 + 33x(x^2+60) + 272x^2)] - 3x^2= 4(x^2+60)^2 + 132x(x^2+60) + 1085x^2= [2(x^2 +60) + 35x][2(x^2 +60) + 31x]= (2x^2 + 35x + 120)(2x^2 + 31x + 120)= (2x^2 + 35x + 120)(2x + 15)(x+8)2。xy(x^2-y^2)+yz(y^2-z^2)+zx(z^2-x^2) =x^3y-xy^3+y^3z-yz^3+z^3x-zx^3 =x^3(y-z)+y^3(z-x)+z^3(x-y) 因为x-y=(x-z)+(z-y),所以：=x^3(y-z)+y^3(z-x)+z^3[(x-z)+(z-y)] =(x^3-z^3)(y-z)+(y^3-z^3)(z-x) =(x-z)(x^2+xz+z^2)(y-z)+(y-z)(y^2+yz+z^2)(z-x) =(x-z)(y-z)(x^2+zx+z^2-y^2-yz-z^2) =(x-z)(y-z)(x-y)(x+y+z) 3。x^2+3xy-2y^2-x+8y-6=(x+2y)(2x-y)-x+8y-6=(x+2y)(2x-y)-(x-8y)-6=(x+2y-2)(2x-y+3) （十字相乘法）[也可用待定系数法令(x+2y)(2x-y)-(x-8y)-6=(x+2y+a)(2x-y+b) }