题目

10道因式分解
1.-7m(m-n)^3+21mn(n-m)^2
2.5x(x-2y)^2-10y(2y-x)^2
3.225(x-y)^2-196(x+y)^2
4.(5x-3y)^2-(3x-5y)^2
5.(5m^2+8n^2)^2-(4m^2+n^2)^2
6.x^3+x^2y-xy^2-y^3
7.9m^2-15m+4分之25
8.(a^2-1)^2+6(1-a^2)+9
9.a^2-9b^2+6b-1
10.mn^2-2mn+2n-4

提问时间：2021-03-28

答案

1.-7m(m-n)^3+21mn(n-m)^2
=-7m(m-n)^3+21mn(m-n)^2
=-7m(m-n)^2[(m-n)-3n]
=-7m(m-n)^2(m-4n)
2.5x(x-2y)^2-10y(2y-x)^2
=5x(x-2y)^2-10y(x-2y)^2
=5(x-2y)^3(x-2y)
3.225(x-y)^2-196(x+y)^2
=[15(x-y)]²-[14(x+y)^2
=[15(x-y)+14(x+y)][15(x-y)-14(x+y)]
=(15x-15y+14x+14y)(15x-15y-14x-14y)
=(29x-y)(x-29y)
4.(5x-3y)^2-(3x-5y)^2
=[(5x-3y)+(3x-5y)][(5x-3y)-(3x-5y)]
=(8x-8y)(2x+2y)
=16(x-y)(x+y)
5.(5m^2+8n^2)^2-(4m^2+n^2)^2
=(5m^2+8n^2+4m^2+n^2)(5m^2+8n^2-4m^2-4n^2)
=(9m^2+9n^2)(m^2+4n^2)
=9(m^2+n^2)(m^2+4n^2)
6.x^3+x^2y-xy^2-y^3
=(x^3+x^2y)-(xy^2+y^3)
=x^2(x+y)-y^2(x+y)
=(x+y)(x^2-y^2)
=(x+y)(x+y)(x-y)
=(x-y)(x+y)^2
7.9m^2-15m+4分之25
=(3m)^2-15m+(5/2)^2
=(3m-5/2)^2
8.(a^2-1)^2+6(1-a^2)+9
=(a^2-1)^2-6(a^2-1)+9
=(a^2-1-3)^2
=(a^2-4)^2
=(a+2)^2(a-2)^2
9.a^2-9b^2+6b-1
=a^2-(9b^2-6b+1)
=a^2-(3b-1)^2
=(a+3b-1)(a-3b+1)
10.mn^2-2mn+2n-4
=(mn^2-2mn)+(2n-4)
=mn(n-2)+2(n-2)
=(n-2)(mn+2)