erweitern (x^2+pi)^4

Lösung

erweitern

(x^{2} + π)^{4}

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

Schritte zur Lösung

(x^{2} + π)^{4}

Wende Binomialsetz an:

(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}

Erweitere Summation

= \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}

Vereinfache

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

Vereinfache

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

Vereinfache

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

Vereinfache

\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}

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

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

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

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

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