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

Lösung

vereinfachen

(2 x^{2} - y)^{3} - (2 x - y^{2})^{3} + 2 x y (3 x + y)

8 x^{6} + y^{6} - 12 x^{4} y - y^{3} - 8 x^{3} + 18 x^{2} y^{2} - 6 x y^{4} + 6 x^{2} y + 2 x y^{2}

Schritte zur Lösung

(2 x^{2} - y)^{3} - (2 x - y^{2})^{3} + 2 x y (3 x + y)

Schreibe

(2 x^{2} - y)^{3}

um:

8 x^{6} - 12 x^{4} y + 6 x^{2} y^{2} - y^{3}

= 8 x^{6} - 12 x^{4} y + 6 x^{2} y^{2} - y^{3} - (2 x - y^{2})^{3} + 2 x y (3 x + y)

Schreibe

- (2 x - y^{2})^{3}

um:

- 8 x^{3} + 12 x^{2} y^{2} - 6 x y^{4} + y^{6}

= 8 x^{6} - 12 x^{4} y + 6 x^{2} y^{2} - y^{3} - 8 x^{3} + 12 x^{2} y^{2} - 6 x y^{4} + y^{6} + 2 x y (3 x + y)

Schreibe

2 x y (3 x + y)

um:

6 x^{2} y + 2 x y^{2}

= 8 x^{6} - 12 x^{4} y + 6 x^{2} y^{2} - y^{3} - 8 x^{3} + 12 x^{2} y^{2} - 6 x y^{4} + y^{6} + 6 x^{2} y + 2 x y^{2}

Fasse gleiche Terme zusammen

= 8 x^{6} + y^{6} - 12 x^{4} y - y^{3} - 8 x^{3} + 6 x^{2} y^{2} + 12 x^{2} y^{2} - 6 x y^{4} + 6 x^{2} y + 2 x y^{2}

Addiere gleiche Elemente:

6 x^{2} y^{2} + 12 x^{2} y^{2} = 18 x^{2} y^{2}

= 8 x^{6} + y^{6} - 12 x^{4} y - y^{3} - 8 x^{3} + 18 x^{2} y^{2} - 6 x y^{4} + 6 x^{2} y + 2 x y^{2}

s im pl i f y (x^{2} \cdot e^{a \cdot x^{3}})^{2}

s im pl i f y \frac{1}{9 - ( \frac{1}{10} ) ^{n}}

e x p an d (4 x^{3} - 8 y^{2})^{3}

s im pl i f y \frac{( 4 ^{6} \cdot a ^{4} \cdot b ^{2} )}{( 2 ^{8} \cdot a ^{3} \cdot b ^{2} )}

s im pl i f y \frac{( n - 1 ) ! ( n - 2 ) !}{( n ! ) ^{2}}