erweitern 3(x+Δx)^4+(2(x+Δx)-1)^2

Lösung

erweitern

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

3 x^{4} + 12Δ x^{4} + 18 Δ^{2} x^{4} + 12 Δ^{3} x^{4} + 3 Δ^{4} x^{4} + 8Δ x^{2} + 4 Δ^{2} x^{2} - 4Δ x + 4 x^{2} - 4 x + 1

Schritte zur Lösung

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

(x + Δ x)^{4} = x^{4} + 4Δ x^{4} + 6 Δ^{2} x^{4} + 4 Δ^{3} x^{4} + Δ^{4} x^{4}

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

Multipliziere aus

2 (x + Δ x) - 1 : 2 x + 2Δ x - 1

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

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

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

Multipliziere aus

3 (x^{4} + 4Δ x^{4} + 6 Δ^{2} x^{4} + 4 Δ^{3} x^{4} + Δ^{4} x^{4}) : 3 x^{4} + 12Δ x^{4} + 18 Δ^{2} x^{4} + 12 Δ^{3} x^{4} + 3 Δ^{4} x^{4}

= 3 x^{4} + 12Δ x^{4} + 18 Δ^{2} x^{4} + 12 Δ^{3} x^{4} + 3 Δ^{4} x^{4} + (2 x + 2Δ x - 1) (2 x + 2Δ x - 1)

Multipliziere aus

(2 x + 2Δ x - 1) (2 x + 2Δ x - 1) : 8Δ x^{2} + 4 Δ^{2} x^{2} - 4Δ x + 4 x^{2} - 4 x + 1

= 3 x^{4} + 12Δ x^{4} + 18 Δ^{2} x^{4} + 12 Δ^{3} x^{4} + 3 Δ^{4} x^{4} + 8Δ x^{2} + 4 Δ^{2} x^{2} - 4Δ x + 4 x^{2} - 4 x + 1

e x p an d \frac{2 g ( h - g )}{g h - j}

e x p an d - 20 (8 e - 20)

e x p an d \frac{10 ( 7 - 1 )}{7}

e x p an d - \frac{2 ( 45 + 8885 )}{49}

e x p an d \frac{x - 20000}{100 ( x - 200 )}