因式分解（只要答案）1、ab-5abc-2a+10ac2、ab-bc+ac-b²3、x²-27-xy+2x4、8ax+12ax-10bx-15bz6、a^4+a²-ab³-ab7、xy-xz-y²+2yz-z²8、x²-xy+4x-4y9、x³+3x²-4x-1210、x³+6x²+11x+611、2x^3n

Question

因式分解（只要答案）
1、ab-5abc-2a+10ac
2、ab-bc+ac-b²
3、x²-27-xy+2x
4、8ax+12ax-10bx-15bz
6、a^4+a²-ab³-ab
7、xy-xz-y²+2yz-z²
8、x²-xy+4x-4y
9、x³+3x²-4x-12
10、x³+6x²+11x+6
11、2x^3n -12x^2n y^2 +18x^n y^4
12、(ax+by)^2 +(ay-bx)^2 +c^2 x^2+c^2 y^2
13、x^2n +x^n -1/9y^2 +1/4
14、(x^2 +y^2)^3 +(z^2 -x^2)^3-(y^2 +z^2)^3
15、x^6 +64y^6 +12x^2 y^2 -1

Answer 1

1、ab-5abc-2a+10ac=ab(1-5c)-2a(1-5c)=a(1-5c)(b-2)
2、ab-bc+ac-b²=a(b+c)-b(b+c)=(b+c)(a-b)
3、x²-27-xy+2x 这个题目是错的
4、8ax+12ax-10bx-15bz 这个题目是错的
6、a^4+a²-ab³-ab=a(a³-b³)+a(a-b)=a(a-b)(a²+ab+b²)+a(a-b)=a(a-b)(a²-ab+b²+1)
7、xy-xz-y²+2yz-z²=x(y-z)-(y-z)²=(y-z)(x-y+z)
8、x²-xy+4x-4y=x(x-y)+4(x-y)=(x-y)(x+4)
9、x³+3x²-4x-12=x²(x+3)-4(x+3)=(x+3)(x-2)(x+2)
10、x³+6x²+11x+6=x³+6x²+9x+2x+6=(x+3)²+2(x+3)=(x+3)(x+5)
11、2x^4n -12x^2n y^2 +18x^n y^4=2x^n(x^4-6x²y²+9y^4)=2x^n(x²-3y²)²
12、(ax+by)^2 +(ay-bx)^2 +c^2 x^2+c^2 y^2
13、x^2n +x^n -1/9y^2 +1/4=(x^n+1/2)²-1/9y²=(x^n+1/2-1/3y)(x^n+1/2+1/3y)
14、(x^2 +y^2)^3 +(z^2 -x^2)^3-(y^2 +z^2)^3
=(x²+y²+z²-x²)[(x²+y²)²-(x²+y²)(z²-x²)+(z²-x²)²]-(y²+z²)³
=(y²+z²)(x^4+2x²y²+y^4-x²z²-y²z²+x^4+x²y²+z^4-2x²z²+x^4)-(y²+z²)³
=(y²+z²)(3x^4+3x²y²-3x²z²-y²z²+y^4+z^4-y^4-2y²z²-z^4)
=(y²+z²)(3x^4+3x²y²-3x²z²-3y²z²)
=3(y²+z²)(x²+y²)(x²-z²)