分解因式~~

来源:百度知道 编辑:UC知道 时间:2024/06/30 03:10:17
(1)y(2y+1)-y(y-1)+1
(2)2x(2x-y)+y(y-2x)
(3)2y(y-2)-y(y-4)-1
(4)x(x+8)-8(x+2)

过程

(1)y(2y+1)-y(y-1)+1
=2y^2+y-y^2+y+1
=y^2+2y+1
=(y+1)^2

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

(3)2y(y-2)-y(y-4)-1
=2y^2-4y-y^2+4y-1
=y^2-1
=(y+1)(y-1)

(4)x(x+8)-8(x+2)
=x^2+8x-8x-16
=x^2-16
=(x+4)(x-4)

(1)y(2y+1)-y(y-1)+1
=y^2+2y+1
=(y+1)^2

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

(3)2y(y-2)-y(y-4)-1
=y^2-1
=(y-1)(y+1)

(4)x(x+8)-8(x+2)
=x^2-16
=(x-4)(x+4)

1:(y+1)^2
2:(2*x-y)^2
3:(y-1)*(y+1)
4:(x-4)*(x+4)

1 2y^2+y-y^2+y+1=y^2+2y+1=(y+1)^2
2 4x^2-2xy+y^2-2xy=4x^2-4xy+y^2=(2x-y)^2
3 2y^2-4y-y^2+4y-1=y^2-1^2=(y+1)(y-1)
4 x^2+8x-8x-16=x^2-4^2=(x+4)(x-4)

("x^2"读作 "x的平方")