万急!几道初一十字交叉法的因式分解题1.（x^2+4x）^2-x^2-4x-202.m^2+11n-mn-11m3.9-a^2-b^2-2ab4.9m^2-6m+2n-n^25.ax^2-bx^2-bx+ax+a-b6.x^3+2xy-x-xy^27.a^2+2ab+b^2-2a-2b+1

Question

万急!几道初一十字交叉法的因式分解题
1.（x^2+4x）^2-x^2-4x-20
2.m^2+11n-mn-11m
3.9-a^2-b^2-2ab
4.9m^2-6m+2n-n^2
5.ax^2-bx^2-bx+ax+a-b
6.x^3+2xy-x-xy^2
7.a^2+2ab+b^2-2a-2b+1

Answer 1

1.（x^2+4x）^2-x^2-4x-20
=(x^2+4x)^2 - (x^2+4x) -20
=[(x^2+4x)-5)][(x^2+4x)+4]
=(x+5)(x-1)(x+2)^2
2.m^2+11n-mn-11m
=(m^2-11m) -(mn-11n)
=m(m-11)-n(m-11)
=(m-11)(m-n)
3.9-a^2-b^2-2ab
=9-(a^2+2ab+b^2)
=3^2-(a+b)^2
=(3+a+b)(3-a-b)
4.9m^2-6m+2n-n^2
=(9m^2-6m+1)-(n^2-2n+1)
=(3m-1)^2-(n-1)^2
=(3m-1+n-1)(3m-1-n+1)
=(3m+n-2)(3m-n)
5.ax^2-bx^2-bx+ax+a-b
=x^2(a-b)+x(a-b)+(a-b)
=(a-b)(x^2+x+1)
6.x^3+2xy-x-xy^2
=x(x^2-y^2+2y-1)
=x[x^2-(y-1)^2]
=x(x+y-1)(x-y+1)
7.a^2+2ab+b^2-2a-2b+1
=(a+b)^2-2(a+b)+1
=(a+b-1)^2