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22 tháng 7 2017

a) \(x^3+y^3+z^3-3xyz\)

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

\(=\left[\left(x+y\right)^3+z^3\right]-\left[3xy\left(x+y\right)+3xyz\right]\)

\(=\left(x+y+z\right)\left[\left(x+y\right)^2-xz-yz+z^2\right]-3xy\left(x+y+z\right)\)

\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-xz-yz\right)\)

b) \(x^4+2011x^2+2010x+2011\)

\(=x^4+2010x^2+x^2+2010x+2010+1\)

\(=\left(x^4+x^2+1\right)+\left(2010x^2+2010x+2010\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+1\right)+2010\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2011\right)\)

5 tháng 9 2018

\(x^3+y^3+z^3-3xyz\)

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

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

\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)

26 tháng 11 2021

=(x4−x3+2011x2)+

 

(x3−x2+2011x)+(x2−x+2011)

=x2(x2−x+2011)+x(x2−x+2011)+(x2−x+2011)

=(x2+x+1)(x2−x+2011)

=(x4−x3+2011x2)+(x3−x2+2011x)+(x2−x+2011)

=x2(x2−x+2011)+x(x2−x+2011)+(x2−x+2011)

=(x2+x+1)(x2−x+2011)

 

 

 

 

 

 

 

x3−x2+2011x)+(x2−x+2011)

=x2(x2−x+2011)+x(x2−x+2011)+(x2−x+2011)=(x2+x+1)(x2−x+2011)

 

 

 

 

 

26 tháng 11 2021

seo gần nhau hía:>

18 tháng 10 2021

\(a,\Rightarrow\left(x-3-5+2x\right)\left(x-3+5-2x\right)=0\\ \Rightarrow\left(3x-8\right)\left(2-x\right)=0\Rightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{8}{3}\end{matrix}\right.\\ b,=\left(x+y\right)^2-\left(x-2y\right)^2\\ =\left(x+y-x+2y\right)\left(x+y+x-2y\right)=3y\left(2x-y\right)\\ c,=\left(x+y-x+y\right)\left(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2\right)\\ =2y\left(3x^2+y^2\right)\\ d,=\left(x+y\right)^3-3xy\left(x+y\right)+z^3-3xyz\\ =\left(x+y+z\right)\left(x^2+2xy+y^2-xz-yz+z^2\right)-3xy\left(x+y+z\right)\\ =\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-xz\right)\)

4 tháng 12 2014

= x3 + y3 + z3 + 3x2yz + 3xy2z + 3xyz2 - x3 -y3 - z3

=3x2yz + 3xy2z + 3xyz2

= 3xyz( x + y + z)

4 tháng 12 2014

b.

x^4+2012x^2+2012x-x+2012=

(x^4-x)+2012(x^2+x+1)=

x(x-1)(x^2+x+1)+2012(x^2+x+1)=

(x+2012)(x^2+x+1)

 

2 tháng 9 2016

a ) \(3x^3-7x^2+17x-5\)

\(=\left(3x^2-x^2\right)-\left(6x^2-2x\right)+\left(15x-5\right)\)

\(=x^2\left(3x-1\right)-2x\left(3x-1\right)+5\left(3x-1\right)\)

\(=\left(x^2-2x+5\right)\left(3x-1\right)\)

\(x^4+2011x^2+2010x+2011\)

\(=x^4-x+2011x^2+2011x+2011\)

\(=x\left(x^3-1\right)+2011\left(x^2+x+1\right)\)

\(=x\left(x-1\right)\left(x^2+x+1\right)+2011\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2011\right)\)

8 tháng 6 2015

x4+2011x2+2010x+2011

=(x4+x3+x2)+(2011x2+2011x+2011)-(x3+x2+x)

=x2(x2+x+1)+2011(x2+x+1)-x(x2+x+1)

=(x2+x+1)(x2+2011-x)

8 tháng 6 2015

x4+2011x2+2010x+2011=x4-x+2011x2+2011x+2011

                                    =x(x3-1)+2011(x2+x+1)

                                    =x(x- 1)(x2+x+1)+2011(x2+x+1)

                                   =(x2+x+1)[x(x-1)+2011]

                                    =(x2+x+1)(x2-x+2011)

13 tháng 12 2020

a) (x  + y + z)3 - x3 - y3 - z3

= (x + y + z)3 - z3 - (x3 + y3

= (x + y + z - z)[(x + y + z)2 + (x + y + z).z + z2) - (x + y)(x2 - xy + y2)

= (x + y)(x2 + y2 + z2 + 2xy + 2yz + 2zx + 2xz + 2yz + z2 + z2) - (x + y)(x2 - xy + y2)

= (x + y)(x2 + y2 + 3z2 + 2xy + 4yz + 4zx) - (x + y)(x2 - xy + y2)

= (x + y)(3z2 + 3xy + 5yz + 4zx) 

b) Sửa đề x4 + 2010x2 + 2009x + 2010

= (x4 + x2 + 1) + (2009x2 + 2009x + 2009)

= (x4 + 2x2 + 1 - x2) + 2009(x2 + x + 1)

= [(x2 + 1)2 - x2] + 2009(x2 + x + 1)

= (x2 + x + 1)(x2 - x + 1) + 2009(x2 + x + 1)

= (x2 + x + 1)(x2 - x + 2010)

1 tháng 9 2020

a) \(\left(x+y+z\right)^3-x^3-y^3-z^3\)

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

\(=\left[\left(x+y\right)^3+z^3+3.\left(x+y\right).z.\left(x+y+z\right)\right]-x^3-y^3-z^3\)

\(=\left[x^3+y^3+3xy.\left(x+y\right)+z^3+3\left(x+y\right).z.\left(x+y+z\right)\right]-x^3-y^3-z^3\)

\(=3xy\left(x+y\right)+3\left(x+y\right)z.\left(x+y+z\right)\)

\(=3.\left(x+y\right)\left(xy+zx+zy+z^2\right)\)

\(=3.\left(x+y\right)\left(y+z\right)\left(z+x\right)\)

b) \(x^4+2012x^2+2011x+2012\)

\(=x^4-x+2012x^2+2012x+2012\)

\(=x.\left(x^3-1\right)+2012.\left(x^2+x+1\right)\)

\(=x.\left(x-1\right)\left(x^2+x+1\right)+2012.\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2012\right)\)