erweitern (x^2+y^2-1)^5

Lösung

erweitern

(x^{2} + y^{2} - 1)^{5}

x^{10} + 5 x^{8} y^{2} - 5 x^{8} + 10 x^{6} y^{4} - 20 x^{6} y^{2} + 10 x^{6} + 10 x^{4} y^{6} - 30 x^{4} y^{4} + 30 x^{4} y^{2} - 10 x^{4} + 5 x^{2} y^{8} - 20 x^{2} y^{6} + 30 x^{2} y^{4} - 20 x^{2} y^{2} + 5 x^{2} + y^{10} - 5 y^{8} + 10 y^{6} - 10 y^{4} + 5 y^{2} - 1

Schritte zur Lösung

(x^{2} + y^{2} - 1)^{5}

(x^{2} + y^{2} - 1)^{5} = (x^{2} + y^{2} - 1) (x^{2} + y^{2} - 1) (x^{2} + y^{2} - 1) (x^{2} + y^{2} - 1) (x^{2} + y^{2} - 1)

= (x^{2} + y^{2} - 1) (x^{2} + y^{2} - 1) (x^{2} + y^{2} - 1) (x^{2} + y^{2} - 1) (x^{2} + y^{2} - 1)

Multipliziere aus

(x^{2} + y^{2} - 1) (x^{2} + y^{2} - 1) (x^{2} + y^{2} - 1) (x^{2} + y^{2} - 1) (x^{2} + y^{2} - 1) : x^{10} + 5 x^{8} y^{2} - 5 x^{8} + 10 x^{6} y^{4} - 20 x^{6} y^{2} + 10 x^{6} + 10 x^{4} y^{6} - 30 x^{4} y^{4} + 30 x^{4} y^{2} - 10 x^{4} + 5 x^{2} y^{8} - 20 x^{2} y^{6} + 30 x^{2} y^{4} - 20 x^{2} y^{2} + 5 x^{2} + y^{10} - 5 y^{8} + 10 y^{6} - 10 y^{4} + 5 y^{2} - 1

= x^{10} + 5 x^{8} y^{2} - 5 x^{8} + 10 x^{6} y^{4} - 20 x^{6} y^{2} + 10 x^{6} + 10 x^{4} y^{6} - 30 x^{4} y^{4} + 30 x^{4} y^{2} - 10 x^{4} + 5 x^{2} y^{8} - 20 x^{2} y^{6} + 30 x^{2} y^{4} - 20 x^{2} y^{2} + 5 x^{2} + y^{10} - 5 y^{8} + 10 y^{6} - 10 y^{4} + 5 y^{2} - 1

e x p an d (x + d x)^{4}

e x p an d (4 x^{2} y + 2 x) (3 ab c - d e f x)

e x p an d \frac{81 ( n + 1 ) ^{2}}{4 n ^{2}}

e x p an d \frac{1}{( s + 2 ) ( s ^{2} + 2 s + 3 )}

e x p an d (1 + ln (x)) d x + (1 + ln (y)) d y