1。
x(a-b)(b-c)-y(b-a)(b-c)
=x(a-b)(b-c) y(a-b)(b-c)
=(a-b)[x(b-c) y(b-c)]
=(a-b)(b-c)(x y)
2。
x^4-81
=(x^2-9)(x^2 9)
=(x-3)(x 3)(x^2 9)
3。
a^2/4-ab b^2=(a/2-b)^2
4。
2x^3-18xy^2
=2x(x^2-9y^2)
=2x(x-3y)(x 3y)
5。
-y^3-1/4y y^2
=-(y^3 1/4y-y^2)
=-y(y^2 1/4-y)
=-y(y-1/2)^2
6。
-8x^2 10x=0
8x^2-10x=0
4x^2-5x=0
x(4x-5)=0
x1=0,x2=5/4
7。
4x^2=(3x-1)^2
4x^2-(3x-1)^2=0
[2x-(3x-1)][2x (3x-1)]=0
(-x 1)(5x-1)=0
x1=1,x2=1/5
8。
[(3x-7)^2-(x 5)^2]梅(4x-24)
=[(3x-7)-(x 5)][(3x-7) (x 5)]梅(4x-24)
=(3x-7-x-5)(3x-7 x 5)梅(4x-24)
=(2x-12)(4x-2)梅(4x-24)
=2(x-6)(4x-2)梅4(x-6)
=4(x-6)(2x-1)梅4(x-6)
=2x-1
9。
[(x^2 y^2)-(x-y)^2 2y(x-y)]梅4y
=[(x^2 y^2)-(x^2-2xy y^2) (2xy-2y^2)]梅4y
=[(x^2 y^2-x^2 2xy-y^2) (2xy-2y^2)]梅4y
=(2xy 2xy-2y^2)梅4y
=(4xy-2y^2)梅4y
=2y(2x-y)梅4y
=(2x-y)/2。
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