erweitern (a+bx+cy+dx^2+ey^2+fxy)^2

Lösung

erweitern

(a + b x + cy + d x^{2} + e y^{2} + f x y)^{2}

2 a d x^{2} + 2 b d x^{3} + d^{2} x^{4} + 2 e d x^{2} y^{2} + 2 c d x^{2} y + 2 d x^{3} y f + 2 ab x + b^{2} x^{2} + 2 e b x y^{2} + 2 b c x y + 2 a x y f + 2 b x^{2} y f + 2 c x y^{2} f + 2 e x y^{3} f + x^{2} y^{2} f^{2} + a^{2} + 2 e a y^{2} + e^{2} y^{4} + 2 a cy + c^{2} y^{2} + 2 ec y^{3}

Schritte zur Lösung

(a + b x + cy + d x^{2} + e y^{2} + f x y)^{2}

= (a + b x + cy + d x^{2} + e y^{2} + x y f)^{2}

(a + b x + cy + d x^{2} + e y^{2} + f x y)^{2} = (a + b x + cy + d x^{2} + e y^{2} + f x y) (a + b x + cy + d x^{2} + e y^{2} + f x y)

= (d x^{2} + b x + x y f + a + cy + e y^{2}) (d x^{2} + b x + x y f + a + cy + e y^{2})

Multipliziere aus

(a + b x + cy + d x^{2} + e y^{2} + f x y) (a + b x + cy + d x^{2} + e y^{2} + f x y) : 2 a d x^{2} + 2 b d x^{3} + d^{2} x^{4} + 2 e d x^{2} y^{2} + 2 c d x^{2} y + 2 d x^{3} y f + 2 ab x + b^{2} x^{2} + 2 e b x y^{2} + 2 b c x y + 2 a x y f + 2 b x^{2} y f + 2 c x y^{2} f + 2 e x y^{3} f + x^{2} y^{2} f^{2} + a^{2} + 2 e a y^{2} + e^{2} y^{4} + 2 a cy + c^{2} y^{2} + 2 ec y^{3}

= 2 a d x^{2} + 2 b d x^{3} + d^{2} x^{4} + 2 e d x^{2} y^{2} + 2 c d x^{2} y + 2 d x^{3} y f + 2 ab x + b^{2} x^{2} + 2 e b x y^{2} + 2 b c x y + 2 a x y f + 2 b x^{2} y f + 2 c x y^{2} f + 2 e x y^{3} f + x^{2} y^{2} f^{2} + a^{2} + 2 e a y^{2} + e^{2} y^{4} + 2 a cy + c^{2} y^{2} + 2 ec y^{3}

e x p an d 10 c + 10 - (\frac{100 ( 2 c - 8 )}{c ^{2} - 8 c + 20})

e x p an d e^{(y - \frac{( z - y ) ^{2}}{2 l ^{2} - t})}

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

e x p an d 2 (x - 1) + 3 (x - 2 - 5 (x + 3) = 8)

e x p an d \frac{17 y ^{2} - 119 y + 104}{( 5 y - 3 ) ( y - 5 ) ^{2}}