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6 tháng 6 2017

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

17 tháng 6 2017

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

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

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

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

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

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

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

\(=2x^2\)

c) \(\left(x-y+z\right)^2+\left(z-y\right)^2+2\left(x-y+z\right)\left(y-z\right)\)

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

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

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

2 tháng 9 2017

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

= 2x2 + 2y2

b ) 2 . ( x - y ) . ( x + y ) + ( x + y )2 + ( x - y )2

= 2 . ( x2 - y2 ) + x2 + 2xy + y2 + x2 - 2xy + y2

= 2x2 - 2y2 + x2 +2xy + y2 + x2 - 2xy + y2

= 4x2

c ) ( x - y + z )2 - ( z - y )2 + 2.( x - y + z ) ( y - z )

= x2 + y2 + z2 - 2xy + 2 xz - 2yz - z2 + 2zy - y2 + 2xy - y2 + 2yz -2xz + 2y2 - 2z2

= x2

28 tháng 6 2016

1)  2xy2+x2y4+1=(xy2)2+2xy2.1+12=(xy2+1)2

2)

a)2(x-y)(x+y)+(x+y)2+(x-y)2=(x+y+x-y)2=(2x)2=4x2

b)(x-y+z)2+(z-y)2+2(x-y+z)(y-z)

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

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

=x2

27 tháng 7 2016

ngu the

27 tháng 7 2016

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

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

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

\(=x^2\)

14 tháng 6 2016

\(a,2\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2+\left(x-y\right)^2\)

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

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

\(=4x^2\)

a,2(x-y)(x+y)+(x+y)2+(x-y)2

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

=4x2

b,=x2

26 tháng 11 2022

a: \(\dfrac{y}{\left(x-y\right)\left(y-z\right)}-\dfrac{z}{\left(y-z\right)\left(x-z\right)}-\dfrac{x}{\left(x-y\right)\left(x-z\right)}\)

\(=\dfrac{xy-yz-xz+yz-xy+xz}{\left(x-y\right)\left(y-z\right)\left(x-z\right)}\)

=0

c: \(=\dfrac{1}{x\left(x-y\right)\left(x-z\right)}-\dfrac{1}{y\left(y-z\right)\left(x-y\right)}+\dfrac{1}{z\left(x-z\right)\left(y-z\right)}\)

\(=\dfrac{zy\left(y-z\right)-xz\left(x-z\right)+xy\left(x-y\right)}{xyz\left(x-y\right)\left(y-z\right)\left(x-z\right)}\)

\(=\dfrac{zy^2-z^2y-x^2z+xz^2+xy\left(x-y\right)}{xyz\left(x-y\right)\left(y-z\right)\left(x-z\right)}\)

\(=\dfrac{1}{xyz}\)

 

7 tháng 9 2020

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

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

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

7 tháng 9 2020

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

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

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

\(=-z^2\)