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问题: 因式分解

100x+14ay-10bx-14by
x^2y+3x-2x^2y^2
a^2+4a-27
m^2+4m-12
4x^3y^3-9xy-6y
9m^2-6m+2n-n^2

解答:

10ax+14ay-10bx-14by
=10x(a-b)+14y(a-b)
=2(a-b)(5x+7y)
x^2y+3x-2x^2y^2
=x(xy+3-2xy^2)
=x(1+xy)(3-2xy)
a^2+4a-27
=

m^2+4m-12
=(m-2)(m+6)
4x^3y^3-9xy-6y
=y(4x^3y^2-9x-6)
9m^2-6m+2n-n^2
=(3m-1)^2-(n-1)^2
=(3m+n-2)(3m-n)