erweitern (b/a (x-z)+y+c)^3

Lösung

erweitern

(\frac{b}{a} (x - z) + y + c)^{3}

\frac{b ^{3} ( x - z ) ( x - z ) ( x - z )}{a ^{3}} + \frac{3 b ^{2} x ^{2} y + 3 b ^{2} z ^{2} y + 3 b ^{2} x ^{2} c + 3 b ^{2} z ^{2} c - 6 x b ^{2} zy - 2 x b ^{2} cz - 2 c x b ^{2} z - 2 b ^{2} c x z}{a ^{2}} + \frac{3 b x y ^{2} - 3 b z y ^{2} + 3 b x c ^{2} - 3 b z c ^{2} + 6 b c x y - 6 b czy}{a} + y^{3} + 3 c y^{2} + 3 y c^{2} + c^{3}

Schritte zur Lösung

(\frac{b}{a} (x - z) + y + c)^{3}

Vereinfache

(\frac{b}{a} (x - z) + y + c)^{3} : (\frac{b}{a} (x - z) + y + c) (\frac{b}{a} (x - z) + y + c) (\frac{b}{a} (x - z) + y + c)

= (\frac{b}{a} (x - z) + y + c) (\frac{b}{a} (x - z) + y + c) (\frac{b}{a} (x - z) + y + c)

Schreibe

(\frac{b}{a} (x - z) + y + c) (\frac{b}{a} (x - z) + y + c)

um:

\frac{b ^{2} ( x - z ) ( x - z )}{a ^{2}} + \frac{2 b x y - 2 b zy + 2 b c x - 2 b cz}{a} + y^{2} + 2 cy + c^{2}

= (\frac{b ^{2} ( x - z ) ( x - z )}{a ^{2}} + \frac{2 b x y - 2 b zy + 2 b c x - 2 b cz}{a} + y^{2} + 2 cy + c^{2}) (\frac{b}{a} (x - z) + y + c)

Setze Klammern

= \frac{b ^{2} ( x - z ) ( x - z )}{a ^{2}} \cdot \frac{b}{a} (x - z) + \frac{b ^{2} ( x - z ) ( x - z )}{a ^{2}} y + \frac{b ^{2} ( x - z ) ( x - z )}{a ^{2}} c + \frac{2 b x y - 2 b zy + 2 b c x - 2 b cz}{a} \cdot \frac{b}{a} (x - z) + \frac{2 b x y - 2 b zy + 2 b c x - 2 b cz}{a} y + \frac{2 b x y - 2 b zy + 2 b c x - 2 b cz}{a} c + y^{2} \frac{b}{a} (x - z) + y^{2} y + y^{2} c + 2 cy \frac{b}{a} (x - z) + 2 cyy + 2 cyc + c^{2} \frac{b}{a} (x - z) + c^{2} y + c^{2} c

Vereinfache

\frac{b ^{2} ( x - z ) ( x - z )}{a ^{2}} \cdot \frac{b}{a} (x - z) + \frac{b ^{2} ( x - z ) ( x - z )}{a ^{2}} y + \frac{b ^{2} ( x - z ) ( x - z )}{a ^{2}} c + \frac{2 b x y - 2 b zy + 2 b c x - 2 b cz}{a} \cdot \frac{b}{a} (x - z) + \frac{2 b x y - 2 b zy + 2 b c x - 2 b cz}{a} y + \frac{2 b x y - 2 b zy + 2 b c x - 2 b cz}{a} c + y^{2} \frac{b}{a} (x - z) + y^{2} y + y^{2} c + 2 cy \frac{b}{a} (x - z) + 2 cyy + 2 cyc + c^{2} \frac{b}{a} (x - z) + c^{2} y + c^{2} c : \frac{b ^{3} ( x - z ) ( x - z ) ( x - z )}{a ^{3}} + \frac{3 b ^{2} x ^{2} y + 3 b ^{2} z ^{2} y + 3 b ^{2} x ^{2} c + 3 b ^{2} z ^{2} c - 6 x b ^{2} zy - 2 x b ^{2} cz - 2 c x b ^{2} z - 2 b ^{2} c x z}{a ^{2}} + \frac{3 b x y ^{2} - 3 b z y ^{2} + 3 b x c ^{2} - 3 b z c ^{2} + 6 b c x y - 6 b czy}{a} + y^{3} + 3 c y^{2} + 3 y c^{2} + c^{3}

= \frac{b ^{3} ( x - z ) ( x - z ) ( x - z )}{a ^{3}} + \frac{3 b ^{2} x ^{2} y + 3 b ^{2} z ^{2} y + 3 b ^{2} x ^{2} c + 3 b ^{2} z ^{2} c - 6 x b ^{2} zy - 2 x b ^{2} cz - 2 c x b ^{2} z - 2 b ^{2} c x z}{a ^{2}} + \frac{3 b x y ^{2} - 3 b z y ^{2} + 3 b x c ^{2} - 3 b z c ^{2} + 6 b c x y - 6 b czy}{a} + y^{3} + 3 c y^{2} + 3 y c^{2} + c^{3}

e x p an d l {e^{4 t} (t - cos (t))}

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

e x p an d - \frac{100}{( x + 1 ) ^{2}}

s im pl i f y - 2 (3 - 1)

e x p an d \frac{4 - 3 s}{( s ^{2} + 9 ) \cdot 2}