erweitern (12c^2d^3e-11fg^2)(12c^2d^3e+11fg^2)

Lösung

erweitern

(12 c^{2} d^{3} e - 11 f g^{2}) (12 c^{2} d^{3} e + 11 f g^{2})

144 e^{2} c^{4} d^{6} - 121 f^{2} g^{4}

Schritte zur Lösung

(12 c^{2} d^{3} e - 11 f g^{2}) (12 c^{2} d^{3} e + 11 f g^{2})

= (12 e c^{2} d^{3} - 11 f g^{2}) (12 e c^{2} d^{3} + 11 f g^{2})

Wende Formel zur Differenz von zwei Quadraten an:

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

a = 12 c^{2} d^{3} e, b = 11 f g^{2}

= (12 c^{2} d^{3} e)^{2} - (11 f g^{2})^{2}

Vereinfache

(12 c^{2} d^{3} e)^{2} - (11 f g^{2})^{2} : 144 e^{2} c^{4} d^{6} - 121 f^{2} g^{4}

= 144 e^{2} c^{4} d^{6} - 121 f^{2} g^{4}

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

e x p an d \frac{( s + 9 - j ) ( s + 9 + j )}{( s - 8 - j ^{3} ) ( s - 8 + j ^{3} )}

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

e x p an d \frac{5 i ^{9} ( 2 - 3 i )}{2 - 1}

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