Question

几道因式分解，答的又快又准的加20分

a²-4a+4-c²

6x²-17x-10

5x²-13xy-6y²

6（m-n）²-10m+10n-4

x³-2x²y+xy²-x

x²+xy-2y²

都要有过程

Answer 1

a^2-4a+4-c^2
=(a-2)^2 - c^2
=[(a-2)+c][(a-2)-c]
=(a-2+c)(a-2-c)

6x^2-17x-10 =(3x-10)(2x+1)

5x^2-13xy-6y^2 =(x-3y)(5x+2y)

6（m-n）^2-10m+10n-4
=6(m-n）^2 - 10(m-n) - 4
=[(m-n) - 2][6(m-n) + 2]
=2[(m-n) - 2][3(m-n) + 1]
=2(m-n-2)(3m-3n+1)

x^3-2x^2y+xy^2-x
=x[(x^2 - 2xy + y^2) - 1]
=x[(x-y)^2 - 1]
=x{[(x-y)+1][(x-y)-1]}
=x(x-y+1)(x-y-1)

x^2+xy-2y^2 =(x+2y)(x-y)