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20 tháng 10 2021

a: \(x^4+2x^3+x^2=x^2\left(x+1\right)^2\)

b: \(5x^2+5xy-x-y\)

\(=5x\left(x+y\right)-\left(x+y\right)\)

\(=\left(x+y\right)\left(5x-1\right)\)

a: =x^2(x^2+2x+1)

=x^2(x+1)^2

b: =x^3+3x^2y+3xy^2+y^3-x-y

=(x+y)^3-(x+y)

=(x+y)[(x+y)^2-1]

=(x+y)(x+y-1)(x+y+1)

c: =5(x^2-2xy+y^2-4z^2)

=5(x-y-2z)(x-y+2z)

16 tháng 7 2017

a) \(x^4+2x^3+x^2=\left(x^2\right)^2+2.x^2.x+x^2=\left(x^2+x\right)^2\)

b) \(x^3-x+3x^2y+3xy^2+y^3-y=x^3+3x^2y+3xy^2+y^3-x-y\)

\(=\left(x-y\right)^3-\left(x+y\right)\)

c) \(5x^2-10xy+5y^2-20z^2=\left(\sqrt{5}x-\sqrt{5}y\right)^2-20z^2\)

Câu b :

\(x^3-x+3x^2y+3xy^2+y^3-y\)

\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)

\(=\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)

Câu c :

\(5x^2-10xy+5y^2-20z^2\)

\(=5\left(x^2-2xy+y^2\right)-20z^2\)

\(=5\left(x-y\right)^2-20z^2\)

\(=5\left[\left(x-y\right)^2-4z^2\right]\)

\(=5\left(x-y+2z\right)\left(x-y-2z\right)\)

Nhiều thế                  

11 tháng 8 2016

mình làm bài 1 nhé 

kq sau khi thu gọn là A =x^6 -7+3x

13 tháng 12 2021

\(a,14x^2y-21xy^2+28x^2y^2=7xy\left(x-3y+4xy\right)\\ b,x\left(x+y\right)-5x-5y=x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\\ c,10x\left(x-y\right)-8\left(y-x\right)=10x\left(x-y\right)+8\left(x-y\right)=\left(x-y\right)\left(10x+8\right)=2\left(x-y\right)\left(5x+4\right)\)

\(d,\left(3x+1\right)^2-\left(x+1\right)^2=\left(3x+1-x-1\right)\left(3x+1+x+1\right)=2x\left(4x+2\right)=4x\left(2x+1\right)\)\(e,x^3+y^3+z^3-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)+3xyz-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)

8 tháng 8 2017

a) \(x^2-x-y^2-y\)

\(=\left(x^2-y^2\right)-\left(x+y\right)\)

\(=\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)

\(=\left(x+y\right)\left(x-y-1\right)\)

8 tháng 8 2017

a) \(^{x^2-x-y^2-y=\left(x^2-y^2\right)-\left(x+y\right)=\left(x-y\right)\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(x-y-1\right)}\)

b)\(a^3-a^2x-ay=a\left(a^2-a.x-y\right)\)

c)\(5x^2-10xy+5y-20z^2=-20z^2+\left(5-10x\right)y+5x^2 \)

                                                   \(=-5\left(4z^2+2xy-y-x^2\right)\)

d)\(x^3-x+3x^2y+3xy^2+y^3-y\)

\(=\left(x^3+3xy^2+3x^2y+y^3\right)-\left(x+y\right)\)

\(=\left(x+y\right)^3-\left(x+y\right)\)

\(=\left(x+y\right)\left[\left(x+y\right)^2-1\right]=\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\)

10 tháng 8 2016

a.\(x^2\left(x^2+2x+1\right)\)

   \(x^2\left(x+1\right)^2\)

23 tháng 7 2016

1/a ) = (x+y)3 -(x+y)

= (x+y)[(x+y)2+1]

c) = 5(x2-xy+y2)-20z2

=5(x-y)2-20z2

= 5 [ (x-y)2- 4z2 ]

=5(x-y-4z)(x-y+4z)
 

23 tháng 7 2016

Bài 1:

a) x3-x+3x2y+3xy2+y3-y

=x3+2x2y-x2+xy2-xy+x2y+2xy2-xy+y3-y2+x2+2xy-x+y2-y

=x(x2+2xy-x+y2-y)+y(x2+2xy-x+y2-y)+(x2+2xy-x+y2-y)

=(x2+2xy-x+y2-y)(x+y+1)

=[x(x+y-1)+y(x+y-1)](x+y+1)

=(x+y-1)(x+y)(x+y+1) 

c) 5x2-10xy+5y2-20z2

=-5(2xy-y2+4z2-2)

Bài 2:

5x(x-1)=x-1   

=>5x2-6x+1=0

=>5x2-x-5x+1

=>x(5x-1)-(5x-1)

=>(x-1)(5x-1)=0

=>x=1 hoặc x=1/5

b) 2(x+5)-x2-5x=0

=>2(x+5)-x(x+5)=0

=>(2-x)(x+5)=0

=>x=2 hoặc x=-5

Câu 2 nha

\(a,x^4+2x^3+x^2\)

\(=x^2\left(x^2+2x+1\right)\)

\(=x^2\left(x+1\right)^2\)

\(c,x^2-x+3x^2y+3xy^2+y^3-y\)

\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)

\(=\left(x+y\right)^3-\left(x+y\right)\)

\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)