1、分解因式：
4x^2+2x-9y^2-3y
=4x^2-9y^2+2x-3y
=(2x-3y)(2x+3y)+2x-3y
=(2x-3y)(2x+3y+1)
2、分解因式：
x^4-3x^2-4
=(x^2-4)(x^2+1)
=(x-2)(x-2)(x^2+1)
3、多项式8x-x^4,x^5-16x,x^4-4x^3+4x^2的公因式是:x(x-2)
8x-x^4
=-x(x^3-8)
=-x(x-2)(x^2+2x+4)
x^5-16x
=x(x^4-16)
=x(x^2-4)(x^2+4)
=x(x-2)(x+2)(x^2+4)
x^4-4x^3+4x^2
=x^2(x^2-4x+4)
=x^2(x-2)^2
4、已知：m-n=2,m^2+n^2=4,则mn=0
(m-n)^2=m^2+n^2-2mn
2^2=4-2mn
2mn=0
mn=0
5、若1/x-1/y =3.则2x+3xy-2y/x-2xy-y =3/5
1/x - 1/y =3
(y-x)=3xy
x-y=-3xy
(2x+3xy-2y)/(x-2xy-y)
=(-6xy2x+3xy)/(-3xyx-2xy)
=(-3xy)/(-5xy)
=3/5
6、已知：x-1/x=2 ,则x^3-1/x^3+2/x-2x=
(x^3-1)/x^3+2/x-2x
=(x-1/x)(x^2+1+1/x^2)-2(x-1/x)
=2*(x^2+1+1/x^2)-2*2
=2(x^2+1+1/x^2)-4
=2[(x-1/x)^2+2+1]-4
=2*[2^2+3]-4
=2*7-4
=10
7、已知：x^2+8/x^3-8 = a/x-2 +b/x^2+2x+4,则a=1 ,b=-2 .
(x^2+8)/(x^3-8)
a/(x-2) +b/(x^2+2x+4)
=a(x^2+2x+4)/[(x-2)(x^2+2x+4)]+b(x-2)/[(x-2)(x^2+2x+4)]
=[a(x^2+2x+4)+b(x-2)]/[(x-2)(x^2+2x+4)]
=[a(x^2+2x+4)+b(x-2)]/(x^3-8)
=[ax^2+2ax+4a+bx-2b]/(x^3-8)
=[ax^2+(2a+b)x+4a-2b]/(x^3-8)
a=1
4a-2b=8
4-2b=8
b=-2
8、若|a|=-a,则|2a- √a^2|=-3a
|a|=-a
a