erweitern (3x^2+3x-1)^4

Lösung

erweitern

(3 x^{2} + 3 x - 1)^{4}

81 x^{8} + 324 x^{7} + 378 x^{6} - 189 x^{4} + 42 x^{2} - 12 x + 1

Schritte zur Lösung

(3 x^{2} + 3 x - 1)^{4}

Vereinfache

(3 x^{2} + 3 x - 1)^{4} : (3 x^{2} + 3 x - 1) (3 x^{2} + 3 x - 1) (3 x^{2} + 3 x - 1) (3 x^{2} + 3 x - 1)

= (3 x^{2} + 3 x - 1) (3 x^{2} + 3 x - 1) (3 x^{2} + 3 x - 1) (3 x^{2} + 3 x - 1)

Schreibe

(3 x^{2} + 3 x - 1) (3 x^{2} + 3 x - 1)

um:

9 x^{4} + 18 x^{3} + 3 x^{2} - 6 x + 1

= (9 x^{4} + 18 x^{3} + 3 x^{2} - 6 x + 1) (3 x^{2} + 3 x - 1) (3 x^{2} + 3 x - 1)

Schreibe

(9 x^{4} + 18 x^{3} + 3 x^{2} - 6 x + 1) (3 x^{2} + 3 x - 1)

um:

27 x^{6} + 81 x^{5} + 54 x^{4} - 27 x^{3} - 18 x^{2} + 9 x - 1

= (27 x^{6} + 81 x^{5} + 54 x^{4} - 27 x^{3} - 18 x^{2} + 9 x - 1) (3 x^{2} + 3 x - 1)

Setze Klammern

= 27 x^{6} \cdot 3 x^{2} + 27 x^{6} \cdot 3 x + 27 x^{6} (- 1) + 81 x^{5} \cdot 3 x^{2} + 81 x^{5} \cdot 3 x + 81 x^{5} (- 1) + 54 x^{4} \cdot 3 x^{2} + 54 x^{4} \cdot 3 x + 54 x^{4} (- 1) - 27 x^{3} \cdot 3 x^{2} - 27 x^{3} \cdot 3 x - 27 x^{3} (- 1) - 18 x^{2} \cdot 3 x^{2} - 18 x^{2} \cdot 3 x - 18 x^{2} (- 1) + 9 x \cdot 3 x^{2} + 9 x \cdot 3 x + 9 x (- 1) - 1 \cdot 3 x^{2} - 1 \cdot 3 x - 1 \cdot (- 1)

Vereinfache

27 x^{6} \cdot 3 x^{2} + 27 x^{6} \cdot 3 x + 27 x^{6} (- 1) + 81 x^{5} \cdot 3 x^{2} + 81 x^{5} \cdot 3 x + 81 x^{5} (- 1) + 54 x^{4} \cdot 3 x^{2} + 54 x^{4} \cdot 3 x + 54 x^{4} (- 1) - 27 x^{3} \cdot 3 x^{2} - 27 x^{3} \cdot 3 x - 27 x^{3} (- 1) - 18 x^{2} \cdot 3 x^{2} - 18 x^{2} \cdot 3 x - 18 x^{2} (- 1) + 9 x \cdot 3 x^{2} + 9 x \cdot 3 x + 9 x (- 1) - 1 \cdot 3 x^{2} - 1 \cdot 3 x - 1 \cdot (- 1) : 81 x^{8} + 324 x^{7} + 378 x^{6} - 189 x^{4} + 42 x^{2} - 12 x + 1

= 81 x^{8} + 324 x^{7} + 378 x^{6} - 189 x^{4} + 42 x^{2} - 12 x + 1

\int sin (\frac{x}{y}) d x

\frac{\partial}{\partial x} (x^{8 y})

n = 1 \sum \infty ln^{n} (3)

a re a y = 4 - x^{2}, x = - 1, x = 2, y = 0

y^{^{'}} = 2 x y^{3}