erweitern 3(uv^3+w^4)^2+(u+ve^w)^4

Lösung

erweitern

3 (u v^{3} + w^{4})^{2} + (u + v e^{w})^{4}

3 u^{2} v^{6} + 6 u v^{3} w^{4} + 3 w^{8} + u^{4} + 4 e^{w} u^{3} v + 6 e^{2 w} u^{2} v^{2} + 4 e^{3 w} u v^{3} + e^{4 w} v^{4}

Schritte zur Lösung

3 (u v^{3} + w^{4})^{2} + (u + v e^{w})^{4}

(u v^{3} + w^{4})^{2} = u^{2} v^{6} + 2 u v^{3} w^{4} + w^{8}

= 3 (u^{2} v^{6} + 2 u v^{3} w^{4} + w^{8}) + (e^{w} v + u)^{4}

= 3 (u^{2} v^{6} + 2 u v^{3} w^{4} + w^{8}) + (u + e^{w} v)^{4}

(u + v e^{w})^{4} : u^{4} + 4 e^{w} u^{3} v + 6 e^{2 w} u^{2} v^{2} + 4 e^{3 w} u v^{3} + e^{4 w} v^{4}

= 3 (u^{2} v^{6} + 2 u v^{3} w^{4} + w^{8}) + u^{4} + 4 e^{w} u^{3} v + 6 e^{2 w} u^{2} v^{2} + 4 e^{3 w} u v^{3} + e^{4 w} v^{4}

Multipliziere aus

3 (u^{2} v^{6} + 2 u v^{3} w^{4} + w^{8}) : 3 u^{2} v^{6} + 6 u v^{3} w^{4} + 3 w^{8}

= 3 u^{2} v^{6} + 6 u v^{3} w^{4} + 3 w^{8} + u^{4} + 4 e^{w} u^{3} v + 6 e^{2 w} u^{2} v^{2} + 4 e^{3 w} u v^{3} + e^{4 w} v^{4}

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

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

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

s im pl i f y (i - 4)^{6}

e x p an d \frac{x ^{2} + 4}{( x - 3 ) ( x - 5 )}