it

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popolare Algebra >

espandere (x^2+pi)^4

Soluzione

espandere

(x^{2} + π)^{4}

Soluzione

x^{8} + 4 π x^{6} + 6 π^{2} x^{4} + 4 π^{3} x^{2} + π^{4}

Fasi della soluzione

(x^{2} + π)^{4}

Applicare il teorema binomiale:

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

a = x^{2}, b = π

= i = 0 \sum 4 (i 4) (x^{2})^{(4 - i)} π^{i}

Espandere la sommatoria

= \frac{4 !}{0 ! ( 4 - 0 ) !} (x^{2})^{4} π^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (x^{2})^{3} π^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (x^{2})^{2} π^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (x^{2})^{1} π^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (x^{2})^{0} π^{4}

Semplifica

\frac{4 !}{0 ! ( 4 - 0 ) !} (x^{2})^{4} π^{0} : x^{8}

Semplifica

\frac{4 !}{1 ! ( 4 - 1 ) !} (x^{2})^{3} π^{1} : 4 π x^{6}

Semplifica

\frac{4 !}{2 ! ( 4 - 2 ) !} (x^{2})^{2} π^{2} : 6 π^{2} x^{4}

Semplifica

\frac{4 !}{3 ! ( 4 - 3 ) !} (x^{2})^{1} π^{3} : 4 π^{3} x^{2}

\frac{4 !}{4 ! ( 4 - 4 ) !} (x^{2})^{0} π^{4} = π^{4}

= x^{8} + 4 π x^{6} + 6 π^{2} x^{4} + 4 π^{3} x^{2} + π^{4}

Esempi popolari

espandere (ac-db,ad+bc)(e,f)

e x p an d (a c - d b, a d + b c) (e, f)

espandere (x-5)/((x+1)^3)

e x p an d \frac{x - 5}{( x + 1 ) ^{3}}

espandere (y+2)dx+(x-2)dy

e x p an d (y + 2) d x + (x - 2) d y

espandere (g(x+h)-2-x^2)/h

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

espandere-3(-3x^2-7x+4)^2

e x p an d - 3 (- 3 x^{2} - 7 x + 4)^{2}