erweitern (x+y+z+5)^3

Lösung

erweitern

(x + y + z + 5)^{3}

x^{3} + 3 x^{2} y + 3 x^{2} z + 15 x^{2} + 3 x y^{2} + 3 y^{2} z + 30 x y + 3 x z^{2} + 30 x z + 6 x yz + 75 x + y^{3} + 15 y^{2} + 3 y z^{2} + 30 yz + 75 y + z^{3} + 15 z^{2} + 75 z + 125

Schritte zur Lösung

(x + y + z + 5)^{3}

Vereinfache

(x + y + z + 5)^{3} : (x + y + z + 5) (x + y + z + 5) (x + y + z + 5)

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

Schreibe

(x + y + z + 5) (x + y + z + 5)

um:

x^{2} + 2 x y + 2 x z + 10 x + y^{2} + 2 yz + 10 y + z^{2} + 10 z + 25

= (x^{2} + 2 x y + 2 x z + 10 x + y^{2} + 2 yz + 10 y + z^{2} + 10 z + 25) (x + y + z + 5)

Setze Klammern

= x^{2} x + x^{2} y + x^{2} z + x^{2} \cdot 5 + 2 x y x + 2 x yy + 2 x yz + 2 x y \cdot 5 + 2 x z x + 2 x zy + 2 x zz + 2 x z \cdot 5 + 10 xx + 10 x y + 10 x z + 10 x \cdot 5 + y^{2} x + y^{2} y + y^{2} z + y^{2} \cdot 5 + 2 yz x + 2 yzy + 2 yzz + 2 yz \cdot 5 + 10 y x + 10 yy + 10 yz + 10 y \cdot 5 + z^{2} x + z^{2} y + z^{2} z + z^{2} \cdot 5 + 10 z x + 10 zy + 10 zz + 10 z \cdot 5 + 25 x + 25 y + 25 z + 25 \cdot 5

Vereinfache

x^{2} x + x^{2} y + x^{2} z + x^{2} \cdot 5 + 2 x y x + 2 x yy + 2 x yz + 2 x y \cdot 5 + 2 x z x + 2 x zy + 2 x zz + 2 x z \cdot 5 + 10 xx + 10 x y + 10 x z + 10 x \cdot 5 + y^{2} x + y^{2} y + y^{2} z + y^{2} \cdot 5 + 2 yz x + 2 yzy + 2 yzz + 2 yz \cdot 5 + 10 y x + 10 yy + 10 yz + 10 y \cdot 5 + z^{2} x + z^{2} y + z^{2} z + z^{2} \cdot 5 + 10 z x + 10 zy + 10 zz + 10 z \cdot 5 + 25 x + 25 y + 25 z + 25 \cdot 5 : x^{3} + 3 x^{2} y + 3 x^{2} z + 15 x^{2} + 3 x y^{2} + 3 y^{2} z + 30 x y + 3 x z^{2} + 30 x z + 6 x yz + 75 x + y^{3} + 15 y^{2} + 3 y z^{2} + 30 yz + 75 y + z^{3} + 15 z^{2} + 75 z + 125

= x^{3} + 3 x^{2} y + 3 x^{2} z + 15 x^{2} + 3 x y^{2} + 3 y^{2} z + 30 x y + 3 x z^{2} + 30 x z + 6 x yz + 75 x + y^{3} + 15 y^{2} + 3 y z^{2} + 30 yz + 75 y + z^{3} + 15 z^{2} + 75 z + 125

e x p an d x y d x - (1 + x^{2}) d y

e x p an d \frac{x ^{3}}{2 ( 4 - x ^{2} )}

e x p an d 1.25 (4 x - 10 = 7.5)

e x p an d \frac{2 s - 3}{( s - 2 ) ^{2}}

e x p an d \frac{x}{( x + 1 ) ^{2} ( x - 1 )}