5道超级简单的因式分解,要快噢,回答完马上加分

来源:百度知道 编辑:UC知道 时间:2024/09/21 22:31:16
x^4-y^4
x-x^5
(a-b)^2-(a+b)^2
1/9x^2-9/16y^2
-1/4(xy+1)^2+1/16(1-xy)^2

x^4-y^4
=(x^2+y^2)(x^2-y^2)
=(x^2+y^2)(x+y)(x-y)

x-x^5
=x(1-x^4)
=x(1+x^2)(1-x^2)
x(1+x^2)(1+x)(1-x)

(a-b)^2-(a+b)^2
=(a-b+a+b)(a-b-a-b)
=2a*(-2b)
=-4ab

1/9x^2-9/16y^2
=(1/3x+3/4y)(1/3x-3/4y)

-1/4(xy+1)^2+1/16(1-xy)^2
=[1/4(1-xy)+1/2(xy+1)][1/4(1-xy)-1/2(xy+1)]
=[1/4-1/4xy+1/2xy+1/2][1/4-1/4xy-1/2xy-1/2]
=(3/4+1/4xy)(-3/4xy-1/4)

x^4-y^4 =(x^2+y^2)(x^2-y^2)=(x^2+y^2)(x+y)(x-y)
x-x^5 =x(1-x^4)=x(1+x^2)(1-x^2)=x(1+x^2)(1+x)(1-x)
(a-b)^2-(a+b)^2 =[(a-b)+(a+b)][(a-b)-(a+b)]=2a*(-2b)=-4ab
1/9x^2-9/16y^2 =(1/3x+3/4y)(1/3x-3/4y)
-1/4(xy+1)^2+1/16(1-xy)^2=(1/2(xy+1)+1/4(1-xy))(-1/2(xy+1)+1/4(1-xy))=-(xy+3)(3xy+1)/16

1、(x+y)(x-y)(x^2+y^2)
2、x(1+x^2)(1+x)(1-x)
3、-4ab
4、(1/3x+3/4y)(1/3x-3/4y)
5、-(xy+3)(3xy+1)/16