erweitern x^3(sin(y)-x)^2

Lösung

erweitern

x^{3} (sin (y) - x)^{2}

x^{3} sin^{2} (y) - 2 x^{4} sin (y) + x^{5}

Schritte zur Lösung

x^{3} (sin (y) - x)^{2}

Schreibe

(sin (y) - x)^{2}

um:

sin^{2} (y) - 2 x sin (y) + x^{2}

= x^{3} (sin^{2} (y) - 2 x sin (y) + x^{2})

Wende das Distributivgesetz an:

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

x^{3} (sin^{2} (y) - 2 x sin (y) + x^{2}) = x^{3} sin^{2} (y) + x^{3} (- 2 x sin (y)) + x^{3} x^{2}

= x^{3} sin^{2} (y) + x^{3} (- 2 x sin (y)) + x^{3} x^{2}

Vereinfache

x^{3} sin^{2} (y) + x^{3} (- 2 x sin (y)) + x^{3} x^{2} : x^{3} sin^{2} (y) - 2 x^{4} sin (y) + x^{5}

= x^{3} sin^{2} (y) - 2 x^{4} sin (y) + x^{5}

e x p an d \frac{( 2 \cdot s ^{2} + 6 \cdot s + 5 )}{( s + 1 ) ^{2} \cdot ( s + 2 )}

e x p an d \frac{30 x ^{2}}{( 1 + x ^{2} ) ^{2}}

s im pl i f y (x^{2} - 4) (x - 2)

e x p an d (2 x + 1) (2 x + 2Δ x - 1)

e x p an d \frac{3 ( - 3 - x )}{4}