erweitern (16-8x^{1/2}+x)^2

Lösung

erweitern

(16 - 8 x^{\frac{1}{2}} + x)^{2}

x^{2} - 256 x^{\frac{1}{2}} - 16 x^{\frac{3}{2}} + 96 x + 256

Schritte zur Lösung

(16 - 8 x^{\frac{1}{2}} + x)^{2}

Wende Exponentenregel an:

a^{b + c} = a^{b} \cdot a^{c}

(16 - 8 x^{\frac{1}{2}} + x)^{2} = (16 - 8 x^{\frac{1}{2}} + x) (16 - 8 x^{\frac{1}{2}} + x)

= (16 - 8 x^{\frac{1}{2}} + x) (16 - 8 x^{\frac{1}{2}} + x)

Setze Klammern

= 16 \cdot 16 + 16 (- 8 x^{\frac{1}{2}}) + 16 x - 8 x^{\frac{1}{2}} \cdot 16 - 8 x^{\frac{1}{2}} (- 8 x^{\frac{1}{2}}) - 8 x^{\frac{1}{2}} x + x \cdot 16 + x (- 8 x^{\frac{1}{2}}) + xx

Vereinfache

16 \cdot 16 + 16 (- 8 x^{\frac{1}{2}}) + 16 x - 8 x^{\frac{1}{2}} \cdot 16 - 8 x^{\frac{1}{2}} (- 8 x^{\frac{1}{2}}) - 8 x^{\frac{1}{2}} x + x \cdot 16 + x (- 8 x^{\frac{1}{2}}) + xx : x^{2} - 256 x^{\frac{1}{2}} - 16 x^{\frac{3}{2}} + 96 x + 256

= x^{2} - 256 x^{\frac{1}{2}} - 16 x^{\frac{3}{2}} + 96 x + 256

e x p an d 3 x (3 x - 40 + 1 = 0)

e x p an d \frac{7 x + 10}{( x + 1 ) ( x ^{2} - 4 )}

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

e x p an d lo g_{10} \frac{( x + 4 ) ^{5}}{x ^{3}}

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