vereinfachen (5x^2+13x-4)-(17x^2+7x-19)+(5x-7)(3x+1)

Lösung

vereinfachen

(5 x^{2} + 13 x - 4) - (17 x^{2} + 7 x - 19) + (5 x - 7) (3 x + 1)

3 x^{2} - 10 x + 8

Schritte zur Lösung

(5 x^{2} + 13 x - 4) - (17 x^{2} + 7 x - 19) + (5 x - 7) (3 x + 1)

Apply rule:

(a) = a

(5 x^{2} + 13 x - 4) = 5 x^{2} + 13 x - 4

= 5 x^{2} + 13 x - 4 - (17 x^{2} + 7 x - 19) + (5 x - 7) (3 x + 1)

Wende das Distributivgesetz an:

- (a + b) = - a - b

- (17 x^{2} + 7 x - 19) = - 17 x^{2} - 7 x + 19

= 5 x^{2} + 13 x - 4 - 17 x^{2} - 7 x + 19 + (5 x - 7) (3 x + 1)

Schreibe

(5 x - 7) (3 x + 1)

um:

15 x^{2} - 16 x - 7

= 5 x^{2} + 13 x - 4 - 17 x^{2} - 7 x + 19 + 15 x^{2} - 16 x - 7

Fasse gleiche Terme zusammen

= 5 x^{2} - 17 x^{2} + 15 x^{2} + 13 x - 7 x - 16 x - 4 + 19 - 7

Addiere gleiche Elemente:

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

= 3 x^{2} + 13 x - 7 x - 16 x - 4 + 19 - 7

Addiere gleiche Elemente:

13 x - 7 x - 16 x = - 10 x

= 3 x^{2} - 10 x - 4 + 19 - 7

Addiere die Zahlen:

- 4 + 19 - 7 = 8

= 3 x^{2} - 10 x + 8

s im pl i f y x + y + \frac{y ^{2}}{x - y}

s im pl i f y 2 - \frac{1}{2 - \frac{2}{2 + \frac{1}{x}}}

s im pl i f y \frac{3 ^{3}}{3 ^{- 4}}

e x p an d - 2 x - 2 y^{4} \cdot (- x^{5} y - 3) - 5

s im pl i f y \frac{5}{3} + \frac{3}{5}