erweitern (xy+e^z)(x^2+y^2)

Lösung

erweitern

(x y + e^{z}) (x^{2} + y^{2})

x^{3} y + x y^{3} + e^{z} x^{2} + e^{z} y^{2}

Schritte zur Lösung

(x y + e^{z}) (x^{2} + y^{2})

Wende Ausklammerungsregel an (VANI):

(a + b) (c + d) = a c + a d + b c + b d

a = x y, b = e^{z}, c = x^{2}, d = y^{2}

= x y x^{2} + x y y^{2} + e^{z} x^{2} + e^{z} y^{2}

= x^{2} x y + x y^{2} y + e^{z} x^{2} + e^{z} y^{2}

Vereinfache

x^{2} x y + x y^{2} y + e^{z} x^{2} + e^{z} y^{2} : x^{3} y + x y^{3} + e^{z} x^{2} + e^{z} y^{2}

= x^{3} y + x y^{3} + e^{z} x^{2} + e^{z} y^{2}

e x p an d (2 tan (x) + 1) (tan (x) - 2)

e x p an d 2 (x sin (x) + cos (x)) + C

e x p an d (x^{3}) (x^{4})

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

e x p an d π (- \frac{128 2}{5} + 1282)