Question

因式分解（平方差公式）要过程

a^3-ab^2
m^2(x-y)+n^2(y-x)
2-2m^4
3(x+y)^2-27
a^2(b-1)+b^2-b^3
(3m^2-n^2)^2-(m^2-3n^2)^2
("^"就是平方的意思）

Answer 1

=a(a^2-b^2)=a(a+b)(a-b)
=(x-y)(m^2-n^2)=(x-y)(m+n)(m-n)
=2(1-m^4)=2(1+m^2)(1-m^2)=2(1+m)(1-m)(1+m^2)
=3[(x+y)^2-9]=3(x+y+3)(x+y-3)
=(b-1)(a^2-b^2)=(b-1)(a+b)(a-b)
=(3m^2-n^2+m^2-3n^2)(3m^2-n^2-m^2+3n^2)=8(m^2-n^2)(m^2+n^2)=8(m+n)(m-n)(m^2+n^2)
麻烦选我为最佳答案，谢谢，打得很辛苦，希望能帮到你

Answer 2

a^3-ab^2
=a(a²-b²)
=a(a+b)(a-b)

m^2(x-y)+n^2(y-x)
=(x-y)(m²-n²)
=(x-y)(m+n)(m-n)

2-2m^4
=2(1-m^4)
=2(1+m²)(1-m²)
=2(1+m²)(1+m)(1-m)

3(x+y)^2-27
=3[(x+y)²-9)
=3(x+y+3)(x+y-3)

a^2(b-1)+b^2-b^3
=a²(b-1)-b²(b-1)
=(b-1)(a²-b²)
=(b-1)(a+B)(a-b)

(3m^2-n^2)^2-(m^2-3n^2)^2
=(3m²-n²+m²-3n²)(3m²-n²-m²+3n²）
=(4m²-4n²)(2m²+2n²)
=8(m+n)(m-n)(m²+n²)

Answer 3

(1)a^3-ab^2=a(a^2-b^2)=a(a-b)(a+b)
(2)m^2(x-y)+n^2(y-x)=(x-y)(m^2-n^2)=(x-y)(m-n)(m+n)
(3)2-2m^4=2(1-m^4)=2(1-m^2)(1+m^2)=2(1-m)(1+m)(1+m^2)
(4)自己琢磨
（5）a^2(b-1)+b^2-b^3=a^2(b-1)+b^2(1-b)=(a^2-b^2)(b-1)=(a-b)(a+b)(b-1)
(6)和（5）类似。

Answer 4

a^3-ab^2=a(a^2-b^2)=a(a+b)(a-b)
m^2(x-y)+n^2(y-x)=m^2(x-y)-n^2(x-y)=(x-y)(m^2-n^2)=(x-y)(m+n)(m-n)
2-2m^4=2(1-m^4)=2(1+m^2)(1-m^2)=2(1+m^2)(1+m)(1-m)
3(x+y)^2-27=3［(x+y)^2-9］＝3［(x+y)^2-3^2］=3［(x+y+3)(x+y-3)］
a^2(b-1)+b^2-b^3=a^2(b-1)+b^2(1-b)=a^2(b-1)-b^2(b-1)=(b-1)(a^2-b^2)=(b-1)(a+b)(a-b)
(3m^2-n^2)^2-(m^2-3n^2)^2=(3m^2-n^2+m^2-3n^2)(3m^2-n^2-m^2+3n^2)=8(m^2-n^2)(m^2-n^2)=8(m+1)(m-1)(m+1)(m-1)

Answer 5

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