it

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popolare Algebra >

espandere (u-sqrt(1+k)*s)^4

Soluzione

espandere

(u - 1 + k \cdot s)^{4}

Soluzione

u^{4} - 4 u^{3} s 1 + k + 6 k u^{2} s^{2} + 6 u^{2} s^{2} - 4 u s^{3} 1 + k (1 + k) + s^{4} + 2 k s^{4} + s^{4} k^{2}

Fasi della soluzione

(u - 1 + k s)^{4}

Applicare il teorema binomiale:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = u, b = - 1 + k s

= i = 0 \sum 4 (i 4) u^{(4 - i)} (- 1 + k s)^{i}

Espandere la sommatoria

= \frac{4 !}{0 ! ( 4 - 0 ) !} u^{4} (- 1 + k s)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} u^{3} (- 1 + k s)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} u^{2} (- 1 + k s)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} u^{1} (- 1 + k s)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} u^{0} (- 1 + k s)^{4}

Semplificare

\frac{4 !}{0 ! ( 4 - 0 ) !} u^{4} (- 1 + k s)^{0} : u^{4}

Semplificare

\frac{4 !}{1 ! ( 4 - 1 ) !} u^{3} (- 1 + k s)^{1} : - 4 u^{3} s 1 + k

Semplificare

\frac{4 !}{2 ! ( 4 - 2 ) !} u^{2} (- 1 + k s)^{2} : 6 u^{2} s^{2} (k + 1)

Semplificare

\frac{4 !}{3 ! ( 4 - 3 ) !} u^{1} (- 1 + k s)^{3} : - 4 u s^{3} (1 + k)^{3}

Semplificare

\frac{4 !}{4 ! ( 4 - 4 ) !} u^{0} (- 1 + k s)^{4} : s^{4} (1 + k)^{2}

= u^{4} - 4 u^{3} s 1 + k + 6 u^{2} s^{2} (k + 1) - 4 u s^{3} (1 + k)^{3} + s^{4} (1 + k)^{2}

Espandere

6 u^{2} s^{2} (k + 1) : 6 k u^{2} s^{2} + 6 u^{2} s^{2}

= u^{4} - 4 u^{3} s 1 + k + 6 k u^{2} s^{2} + 6 u^{2} s^{2} - 4 u s^{3} (1 + k)^{3} + s^{4} (1 + k)^{2}

Espandere

s^{4} (1 + k)^{2} : s^{4} + 2 k s^{4} + s^{4} k^{2}

= u^{4} - 4 u^{3} s 1 + k + 6 k u^{2} s^{2} + 6 u^{2} s^{2} - 4 u s^{3} (1 + k)^{3} + s^{4} + 2 k s^{4} + s^{4} k^{2}

Semplificare

(1 + k)^{3} : 1 + k (1 + k)

= u^{4} - 4 u^{3} s 1 + k + 6 k u^{2} s^{2} + 6 u^{2} s^{2} - 4 u s^{3} 1 + k (1 + k) + s^{4} + 2 k s^{4} + s^{4} k^{2}

Esempi popolari

espandere s(-6,-2)y(6,6)

e x p an d s (- 6, - 2) y (6, 6)

espandere (14x-28)e^{x^2-4x}

e x p an d (14 x - 28) e^{x^{2} - 4 x}

d/(dt)(({z}(t,x,y))(6x^2+3xy(t)^2))

\frac{d}{d t} ((z (t, x, y)) (6 x^{2} + 3 x y (t)^{2}))

espandere (x-(-1+i))(x-(-1-i))

e x p an d (x - (- 1 + i)) (x - (- 1 - i))

espandere ((XY)+Z)\Rightarrow W

e x p an d ((X Y) + Z) \Rightarrow W