1.解: kx²-6xy-8y²=（2mx+2y)(x-4y)=2m x²-(8m-2)xy-8y².
∴k=2m, 8m-2=6,
∴k=2,m=1.
2.解:9a²-6ab+5b²-4b+5=(9a²-6ab+b²)+(4 b²-4b+1)+4
=(3a-1)²+ (2b-1)²+4＞0.
3.解:令x²+y²=a, ∴a(a-3)=4, ∴x²+y²= a= -1或4.
4. C.(m+n)(m-n).
5.B.2个
6. 4（x+2z)(x-2z)+12xy+9y²=4 x²-16z²+12xy+9y²
=(2x+3y)²-16 z²=(2x+3y+4z) (2x+3y-4z)
=(2×1/2+3×2/3+4×3/4) (2×1/2+3×2/3-4×3/4)=0.
7. 解:∵（a+b+c)²=3(a²+b²+c²）,
∴a²+b²+c²+2ab+2bc+2ca=3a²+3b²+3c².
∴2a²+2b²+2c²-2ab-2bc-2ca=（a-b)²+（b-c)² +（a-c)²=0.
∴a-b=b-c=a-c=0,
∴a=b=c, △ABC是等边三角形.
8. A.ax-bx与by-ax
9. a²-2ab+b²+4a-4b+4= (a-b)²+4(a-b)+4=(a-b+2)².
10.x²(x+1)-y²(y-1)+xy=x的立方+ x²- y的立方+ y²+xy
=( x的立方- y的立方)+ (x²+ y²+xy)
=(x-y) (x²+xy+ y²)+(x²+xy+ y²)=(x-y+1) (x²+xy+ y²).
11. 2a²-(b-2)a-b(b+2)= 2a²-ab+2a- b²-2b
= (a²-ab)+(a²- b²)+(2a--2b)=a(a-b)+ (a+b) (a-b)+2(a-b)
=(a-b) (a+a+b+2)= (a-b) (2a+b+2).
12.（x+1)(x+2)(x-4)(x-5)+9= (x+1) (x-4) (x+2)(x-5)+9
=(x²-3x-4) (x²-3x-10)+9= (x²-3x)²-14(x²-3x)+49
=(x²-3x-7)².
13.解:∵x³-x=5,y³-y=5,
∴x³-y³-x+y=0
∴(x-y) (x²+xy+ y²)-(x-y)= (x-y) (x²+xy+ y²-1)=0.
∵x≠y, ∴x²+xy+ y²-1=0.
∴x²+xy+ y²=1.
14.解:∵a²+b²+c²-ab-bc-ac=0,
∴2a²+2b²+2c²-2ab-2bc-2ac=0,
∴（a-b)²+（b-c)² +（a-c)²=0;
∴a-b=b-c=a-c=0,
∴a=b=c.
上楼的有错,也没我的详细,再说字这么多,好难打哦,要多给分了.