题目因式分解!-3ax+9bx-3by+ay5ax-x+5ay-ymx^3+mx^2y-2nx^3-2nx^2ya(b-c)+a^2-bcm^5-m^4+m^3-2m^2+2m-2x^2-xy-yz+xzx^2(x+y+z)+xyz(2ax+by)^2+(2bx-ay)^2

Question

题目因式分解!
-3ax+9bx-3by+ay
5ax-x+5ay-y
mx^3+mx^2y-2nx^3-2nx^2y
a(b-c)+a^2-bc
m^5-m^4+m^3-2m^2+2m-2
x^2-xy-yz+xz
x^2(x+y+z)+xyz
(2ax+by)^2+(2bx-ay)^2

Answer 1

1.
-3ax+9bx-3by+ay
=-3x(a-3b)+y(a-3b)
=(a-3b)(y-3x)
2.
5ax-x+5ay-y
=x(5a-1)+y(5a-1)
=(5a-1)(x+y)
3.
mx³+mx²y-2nx³-2nx²y
=x²(mx+my-2nx-2ny)
=x²[m(x+y)-2n(x+y)]
=x²(x+y)(m-2n)
4.
a(b-c)+a²-bc
=a²+ab-ac-bc
=a(a+b)-c(a+b)
=(a+b)(a-c)
5.
m^5-m^4+m³-2m²+2m-2
无法分解
6.
x²-xy-yz+xz
=x(x-y)+z(x-y)
=(x-y)(x+z)
7.
x²(x+y+z)+xyz
=x³+x²y+x²z+xyz
=x(x²+x+xz+yz)
8.
(2ax+by)²+(2bx-ay)²
=4a²x²+4abxy+b²y²+4b²x²-4abxy+a²y²
=4a²x²+b²y²+4b²x²+a²y²
=4x²(a²+b²)+y²(a²+b²)
=(a²+b²)(4x²+y²)