vereinfachen (fg^2+6hi)^2

Lösung

vereinfachen

(f g^{2} + 6 hi)^{2}

(f^{2} g^{4} - 36 h^{2}) + 12 f g^{2} hi

Schritte zur Lösung

(f g^{2} + 6 hi)^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

(f g^{2} + 6 hi)^{2} = (f g^{2})^{2} + 2 f g^{2} \cdot 6 hi + (6 hi)^{2}

= (f g^{2})^{2} + 2 f g^{2} \cdot 6 hi + (6 hi)^{2}

(f g^{2})^{2} = f^{2} g^{4}

2 f g^{2} \cdot 6 hi = 12 f g^{2} hi

(6 hi)^{2} = - 36 h^{2}

= f^{2} g^{4} + 12 f g^{2} hi - 36 h^{2}

Rewrite in standard complex form:

(f^{2} g^{4} - 36 h^{2}) + 12 f g^{2} hi

= (f^{2} g^{4} - 36 h^{2}) + 12 f g^{2} hi

s im pl i f y 4 \cdot \frac{9}{4}

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

x 4 x

s im pl i f y \frac{1}{a ^{- 1} + b ^{- 1}}

s im pl i f y 4 x (x)