erweitern (2pirh+2pir^2)^2

Lösung

erweitern

(2 π r h + 2 π r^{2})^{2}

4 π^{2} h^{2} r^{2} + 8 π^{2} h r^{3} + 4 π^{2} r^{4}

Schritte zur Lösung

(2 π r h + 2 π r^{2})^{2}

= (2 πh r + 2 π r^{2})^{2}

Wende Formel für perfekte quadratische Gleichungen an:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = 2 π r h, b = 2 π r^{2}

= (2 π r h)^{2} + 2 \cdot 2 π r h \cdot 2 π r^{2} + (2 π r^{2})^{2}

Vereinfache

(2 π r h)^{2} + 2 \cdot 2 π r h \cdot 2 π r^{2} + (2 π r^{2})^{2} : 4 π^{2} h^{2} r^{2} + 8 π^{2} h r^{3} + 4 π^{2} r^{4}

= 4 π^{2} h^{2} r^{2} + 8 π^{2} h r^{3} + 4 π^{2} r^{4}

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

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

e x p an d (x^{3} + 2 x + 1)^{5}

e x p an d (3 x^{2} + y) d x

e x p an d \frac{( a - 4 ) ( a + 6 )}{6}