Question

几道数学因式分解 求高手帮忙 在线等！！！

1 -x^3y^3+2x^2y^2-xy
2 4x^2-(x^2+1)^2
3 3x^2-3x+四分之三
4 16x^4-y^4
5 8(a-b)^2-12(b-a)
6 25(m-n)^2-9(m+n)^2
求高手帮忙 跪求了 这个是^次方的意思
麻烦过程写详细点 在线等 跪求！！！！！！！！！！！！！！！！！！

Answer 1

1. -x^3y^3+2x^2y^2-xy
=-xy(x^2y^2-2xy+1)
=-xy[(xy)^2-2xy+1]
-xy(xy-1)^2
2.4x^2-(x^2+1)^2
=(2x)^2-(x^2+1)^2
=(2x+x^2+1)(2x-x^2-1)
=-(x+1)^2(x^2-2x+1)
=-(x+1)^2(x-1)^2
3.3x^2-3x+3/4
=3(x^2-x+1/4)
=3(x-1/2)^2
4.16x^4-y^4
=(4x^2)^2-(y^2)^2
=(4x^2+y^2)(4x^2-y^2)
=(4x^2+y^2)(2x+y)(2x-y)
5.8(a-b)^2-12(b-a)
=8(a-b)^2+12(a-b）
=4(a-b)[2(a-b)+3]
=4(a-b)(2a-2b+3)
6. 25(m-n)^2-9(m+n)^2
=[5(m-n)]^2-[3(m+n)]^2
=[5(m-n)+3(m+n)][5(m-n)-3(m+n)]
=(8m-2n)(2m-8n)
=4(4m-n)(m-4n)

Answer 2

1 -x^3y^3+2x^2y^2-xy=-xy(x^2y^2-2xy+1)=-xy(xy-1)^2
2 4x^2-(x^2+1)^2=(2x-x^2-1)(2x+x^2+1)=-(x+1)^2(x-1)^2
3 3x^2-3x+四分之三=3(x^2-x+1/4)=3(x-1/2)^2
4 16x^4-y^4=(4x^2+y^2)(2x+y)(2x-y)
5 8(a-b)^2-12(b-a)=4(a-b)(2a-2b+3)
6 25(m-n)^2-9(m+n)^2=(5m-5n+3m+3n)(5m-5n-3m-3n)=(8m-2n)(2m-8n)=4(4m-n)(m-4n)

Answer 3

-xy（xy+1-2^2）(xy+1+2^2)
-(x^2-1)^2
3(x-1/2)^2
(4x^2+y^2)(2x+y)(2x-y)
4(b-a)(2b-2a-3)
4(4m-n)(m-4n)

Answer 4

1 -x^3y^3+2x^2y^2-xy=-xy(x^2y^2-2xy+1)=-xy(xy-1)^2
2 4x^2-(x^2+1)^2=(2x^2+x^2+1)(2x^-x^2-1)=(3x^2+1)(x^2-1)=(3x^2+1)(x+1)(x-1)
3 3x^2-3x+3/4=3(x^2-x+1/4)=3(x-1/2)^2
4 16x^4-y^4=(4x^2+y^2)(4x^2-y^2)=(4x^2+y^2)(2x+y)(2x-y)
5 8(a-b)^2-12(b-a)=4(a-b)(2a-2b+3)
6 25(m-n)^2-9(m+n)^2=(5(m-n)+3(m+n))(5(m-n)-3(m+n))=(8m-2n)(2m-8n)=4(4m-n)(m-4n)