vereinfachen (4x^3y^2-5x^2y^3+6x^4y-8xy^4)-(12x^2y^3-3xy^4+4x^3y^2-9x^4y)

Lösung

vereinfachen

(4 x^{3} y^{2} - 5 x^{2} y^{3} + 6 x^{4} y - 8 x y^{4}) - (12 x^{2} y^{3} - 3 x y^{4} + 4 x^{3} y^{2} - 9 x^{4} y)

- 17 x^{2} y^{3} + 15 x^{4} y - 5 x y^{4}

Schritte zur Lösung

(4 x^{3} y^{2} - 5 x^{2} y^{3} + 6 x^{4} y - 8 x y^{4}) - (12 x^{2} y^{3} - 3 x y^{4} + 4 x^{3} y^{2} - 9 x^{4} y)

Apply rule:

(a) = a

(4 x^{3} y^{2} - 5 x^{2} y^{3} + 6 x^{4} y - 8 x y^{4}) = 4 x^{3} y^{2} - 5 x^{2} y^{3} + 6 x^{4} y - 8 x y^{4}

= 4 x^{3} y^{2} - 5 x^{2} y^{3} + 6 x^{4} y - 8 x y^{4} - (12 x^{2} y^{3} - 3 x y^{4} + 4 x^{3} y^{2} - 9 x^{4} y)

Wende das Distributivgesetz an:

- (a - b) = - a + b

- (12 x^{2} y^{3} - 3 x y^{4} + 4 x^{3} y^{2} - 9 x^{4} y) = - 12 x^{2} y^{3} + 3 x y^{4} - 4 x^{3} y^{2} + 9 x^{4} y

= 4 x^{3} y^{2} - 5 x^{2} y^{3} + 6 x^{4} y - 8 x y^{4} - 12 x^{2} y^{3} + 3 x y^{4} - 4 x^{3} y^{2} + 9 x^{4} y

Fasse gleiche Terme zusammen

= 4 x^{3} y^{2} - 4 x^{3} y^{2} - 5 x^{2} y^{3} - 12 x^{2} y^{3} + 6 x^{4} y + 9 x^{4} y - 8 x y^{4} + 3 x y^{4}

Addiere gleiche Elemente:

4 x^{3} y^{2} - 4 x^{3} y^{2} = 0

= - 5 x^{2} y^{3} - 12 x^{2} y^{3} + 6 x^{4} y + 9 x^{4} y - 8 x y^{4} + 3 x y^{4}

Addiere gleiche Elemente:

- 5 x^{2} y^{3} - 12 x^{2} y^{3} = - 17 x^{2} y^{3}

= - 17 x^{2} y^{3} + 6 x^{4} y + 9 x^{4} y - 8 x y^{4} + 3 x y^{4}

Addiere gleiche Elemente:

6 x^{4} y + 9 x^{4} y = 15 x^{4} y

= - 17 x^{2} y^{3} + 15 x^{4} y - 8 x y^{4} + 3 x y^{4}

Addiere gleiche Elemente:

- 8 x y^{4} + 3 x y^{4} = - 5 x y^{4}

= - 17 x^{2} y^{3} + 15 x^{4} y - 5 x y^{4}

s im pl i f y \frac{1 - - 1}{1 + - 1}

s im pl i f y \frac{5 x}{2 x}

s im pl i f y \frac{6}{7} + \frac{4}{5}

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

e x p an d (x - 2)^{2} (x - 3)