erweitern (y-x)^2*((4x^2y)/3)

Lösung

erweitern

(y - x)^{2} \cdot (\frac{4 x ^{2} y}{3})

\frac{4 x ^{2} y ^{3} - 8 x ^{3} y ^{2} + 4 x ^{4} y}{3}

Schritte zur Lösung

(y - x)^{2} (\frac{4 x ^{2} y}{3})

Apply rule:

(a) = a

(\frac{4 x ^{2} y}{3}) = \frac{4 x ^{2} y}{3}

= (y - x)^{2} \frac{4 x ^{2} y}{3}

= \frac{4 x ^{2} y}{3} (y - x)^{2}

Schreibe

(y - x)^{2}

um:

y^{2} - 2 y x + x^{2}

= \frac{4 x ^{2} y}{3} (y^{2} - 2 y x + x^{2})

Wende das Distributivgesetz an:

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

\frac{4 x ^{2} y}{3} (y^{2} - 2 y x + x^{2}) = \frac{4 x ^{2} y}{3} y^{2} + \frac{4 x ^{2} y}{3} (- 2 y x) + \frac{4 x ^{2} y}{3} x^{2}

= \frac{4 x ^{2} y}{3} y^{2} + \frac{4 x ^{2} y}{3} (- 2 y x) + \frac{4 x ^{2} y}{3} x^{2}

Vereinfache

\frac{4 x ^{2} y}{3} y^{2} + \frac{4 x ^{2} y}{3} (- 2 y x) + \frac{4 x ^{2} y}{3} x^{2} : \frac{4 x ^{2} y ^{3} - 8 x ^{3} y ^{2} + 4 x ^{4} y}{3}

= \frac{4 x ^{2} y ^{3} - 8 x ^{3} y ^{2} + 4 x ^{4} y}{3}

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

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

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

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

e x p an d (1 - 3) + i (1 + 3)