erweitern (4-x)^{1/2}(1+2x)^2

Lösung

erweitern

(4 - x)^{\frac{1}{2}} (1 + 2 x)^{2}

(4 - x)^{\frac{1}{2}} + (4 - x)^{\frac{1}{2}} \cdot 4 x + (4 - x)^{\frac{1}{2}} \cdot 4 x^{2}

Schritte zur Lösung

(4 - x)^{\frac{1}{2}} (1 + 2 x)^{2}

Schreibe

(1 + 2 x)^{2}

um:

1 + 4 x + 4 x^{2}

= (4 - x)^{\frac{1}{2}} (1 + 4 x + 4 x^{2})

Wende das Distributivgesetz an:

m (a + b + c) = ma + mb + m c

(4 - x)^{\frac{1}{2}} (1 + 4 x + 4 x^{2}) = (4 - x)^{\frac{1}{2}} \cdot 1 + (4 - x)^{\frac{1}{2}} \cdot 4 x + (4 - x)^{\frac{1}{2}} \cdot 4 x^{2}

= (4 - x)^{\frac{1}{2}} \cdot 1 + (4 - x)^{\frac{1}{2}} \cdot 4 x + (4 - x)^{\frac{1}{2}} \cdot 4 x^{2}

Apply rule:

a \cdot 1 = a

(4 - x)^{\frac{1}{2}} \cdot 1 = (4 - x)^{\frac{1}{2}}

= (4 - x)^{\frac{1}{2}} + (4 - x)^{\frac{1}{2}} \cdot 4 x + (4 - x)^{\frac{1}{2}} \cdot 4 x^{2}

e x p an d (y^{\frac{7}{4}} - 1)^{4}

s im pl i f y i (x + y i)^{4}

e x p an d sin (2 t) \cdot x (t - π)

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

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