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العربية

vereinfachen (x-y+z)^2+2(x-y+z)(y-z+x)+(y-z+x)^2

Lösung

vereinfachen

(x - y + z)^{2} + 2 (x - y + z) (y - z + x) + (y - z + x)^{2}

4 x^{2}

Schritte zur Lösung

(x - y + z)^{2} + 2 (x - y + z) (y - z + x) + (y - z + x)^{2}

Schreibe

(x - y + z)^{2}

um:

x^{2} - 2 x y + 2 x z + y^{2} - 2 yz + z^{2}

= x^{2} - 2 x y + 2 x z + y^{2} - 2 yz + z^{2} + 2 (x - y + z) (y - z + x) + (y - z + x)^{2}

Schreibe

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

um:

2 x^{2} - 2 y^{2} + 4 yz - 2 z^{2}

= x^{2} - 2 x y + 2 x z + y^{2} - 2 yz + z^{2} + 2 x^{2} - 2 y^{2} + 4 yz - 2 z^{2} + (y - z + x)^{2}

Schreibe

(y - z + x)^{2}

um:

y^{2} - 2 yz + 2 x y + z^{2} + x^{2} - 2 x z

= x^{2} - 2 x y + 2 x z + y^{2} - 2 yz + z^{2} + 2 x^{2} - 2 y^{2} + 4 yz - 2 z^{2} + y^{2} - 2 yz + 2 x y + z^{2} + x^{2} - 2 x z

Fasse gleiche Terme zusammen

= x^{2} + 2 x^{2} + x^{2} - 2 x y + 2 x y + 2 x z - 2 x z + y^{2} - 2 y^{2} + y^{2} - 2 yz + 4 yz - 2 yz + z^{2} - 2 z^{2} + z^{2}

Addiere gleiche Elemente:

x^{2} + 2 x^{2} + x^{2} = 4 x^{2}

= 4 x^{2} - 2 x y + 2 x y + 2 x z - 2 x z + y^{2} - 2 y^{2} + y^{2} - 2 yz + 4 yz - 2 yz + z^{2} - 2 z^{2} + z^{2}

Addiere gleiche Elemente:

- 2 x y + 2 x y = 0

= 4 x^{2} + 2 x z - 2 x z + y^{2} - 2 y^{2} + y^{2} - 2 yz + 4 yz - 2 yz + z^{2} - 2 z^{2} + z^{2}

Addiere gleiche Elemente:

2 x z - 2 x z = 0

= 4 x^{2} + y^{2} - 2 y^{2} + y^{2} - 2 yz + 4 yz - 2 yz + z^{2} - 2 z^{2} + z^{2}

Addiere gleiche Elemente:

y^{2} - 2 y^{2} + y^{2} = 0

= 4 x^{2} - 2 yz + 4 yz - 2 yz + z^{2} - 2 z^{2} + z^{2}

Addiere gleiche Elemente:

- 2 yz + 4 yz - 2 yz = 0

= 4 x^{2} + z^{2} - 2 z^{2} + z^{2}

Addiere gleiche Elemente:

z^{2} - 2 z^{2} + z^{2} = 0

= 4 x^{2}

s im pl i f y \frac{( 9 a ^{9} - 9 a ^{7} + 18 a ^{4} )}{( 15 a ^{8} )}

s im pl i f y 4 x^{2} - 1 + \frac{2}{( x ^{2} - x - 2 )} - \frac{3}{( x ^{2} - 3 x + 2 )}

s im pl i f y (- 4 x^{3})^{2} \cdot (8 x^{4})^{- 1}

s im pl i f y (p^{- 1} + q^{- 1})^{- 1}

e x p an d (1 - 2 x) (4 + 3 x)