四项因式分解的题.a^2-ab+ac-bc,x^2+ax^2+x+ax-1-a,ac^2+bd^2-ad^2-bc^2,x^2-y^2+ax+ay,x^2-x-9y^2-3y,a^2-b^2+4b-4,a^2-2ab+b^2-c^2,x^2-y^2-z^2+2yz9-4a^2-4ab-b^2 -1-2x-x^2+y^2

Question

四项因式分解的题.
a^2-ab+ac-bc,x^2+ax^2+x+ax-1-a,ac^2+bd^2-ad^2-bc^2,x^2-y^2+ax+ay,
x^2-x-9y^2-3y,a^2-b^2+4b-4,a^2-2ab+b^2-c^2,x^2-y^2-z^2+2yz
9-4a^2-4ab-b^2 -1-2x-x^2+y^2

Answer 1

a^2-ab+ac-bc
=(a^2+ac)-(ab+bc)
=a(a+c)-b(a+c)
=(a-b)(a+c)
x^2+ax^2+x+ax-1-a
=x^2(a+1)+x(a+1)-(a+1)
=(a^2+x-1)(a+1)
ac^2+bd^2-ad^2-bc^2
=(a-b)c^2-(a-b)d^2
=(a-b)(c^2-d^2)
=(a-b)(c-d)(c+d)
x^2-y^2+ax+ay
=(x+y)(x-y)+a(x+y)
=(x+y)(x-y+a)
x^2-x-9y^2-3y
=(x^2-9y^2)-(x+3y)
=(x+3y)(x-3y)-(x+3y)
=(x+3y)(x-3y-1)
a^2-b^2+4b-4
=a^2-(b-2)^2
=(a+b-2)(a-b+2)
a^2-2ab+b^2-c^2
=(a-b)^2-c^2
=(a-b+c)(a-b-c)
x^2-y^2-z^2+2yz
=x^2-(y^2+z^2-2yz)
=x^2-(y-z)^2
=(x+y-z)(x-y+z)
9-4a^2-4ab-b^2
=3^2-(2a-b)^2
=(3+2a-b)(3-2a+b)
-1-2x-x^2+y^2
=y^2-(x+1)^2
=(y+x+1)(y-x-1)